%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET834-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:31:03 AM UTC 2026
% Result : Unsatisfiable 192.52s 53.46s
% Output : Refutation 193.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 301
% Syntax : Number of formulae : 1863 ( 552 unt; 0 typ; 9 def)
% Number of atoms : 4482 (1934 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 19908 (2662 ~;1970 |; 0 &;15276 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 120 ( 117 usr; 18 con; 0-6 aty)
% Number of variables : 4021 ( 0 ^;4003 !; 9 ?;4021 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_Y_decl,type,
v_Y: $i ).
thf(v_X_decl,type,
v_X: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(v_Z_decl,type,
v_Z: $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_Nat_Osize_decl,type,
c_Nat_Osize: $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Wellfounded__Recursion_Owf_decl,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Wellfounded__Relations_Oless__than_decl,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_append_decl,type,
c_append: $i > $i > $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_List_Olistrel_decl,type,
c_List_Olistrel: $i > $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_Divides_Oop_Advd_decl,type,
c_Divides_Oop_Advd: $i > $i > $i > $o ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Oacyclic_decl,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_List_Olex_decl,type,
c_List_Olex: $i > $i > $i ).
thf(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_IntDef_Oint_decl,type,
tc_IntDef_Oint: $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(c_SetInterval_OlessThan_decl,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_decl,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_OatLeast_decl,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(class_Nat_Opower_decl,type,
class_Nat_Opower: $i > $o ).
thf(tc_Datatype_Ooption_decl,type,
tc_Datatype_Ooption: $i > $i ).
thf(c_SetInterval_OgreaterThan_decl,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(c_List_Oset_decl,type,
c_List_Oset: $i > $i > $i ).
thf(tc_Datatype__Universe_Onode_decl,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Datatype__Universe_OIn1_decl,type,
c_Datatype__Universe_OIn1: $i > $i > $i > $i ).
thf(c_Datatype__Universe_Odsum_decl,type,
c_Datatype__Universe_Odsum: $i > $i > $i > $i > $i ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i ).
thf(c_Datatype__Universe_Odprod_decl,type,
c_Datatype__Universe_Odprod: $i > $i > $i > $i > $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_Datatype__Universe_OIn0_decl,type,
c_Datatype__Universe_OIn0: $i > $i > $i > $i ).
thf(c_Sum__Type_OInr_decl,type,
c_Sum__Type_OInr: $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_decl,type,
c_Sum__Type_OInl: $i > $i > $i > $i ).
thf(tc_sum_decl,type,
tc_sum: $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_UNIV_decl,type,
c_UNIV: $i ).
thf(c_IntDef_Oint_decl,type,
c_IntDef_Oint: $i > $i ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(c_Main_OImageE__1_decl,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OPlus_decl,type,
c_Sum__Type_OPlus: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__1_decl,type,
c_Main_OPlusE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OPlusE__2_decl,type,
c_Main_OPlusE__2: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_decl,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_Datatype_Ooption_OSome_decl,type,
c_Datatype_Ooption_OSome: $i > $i > $i ).
thf(c_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Main_ORangeE__1_decl,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $i ).
thf(c_Union_decl,type,
c_Union: $i > $i > $i ).
thf(c_Main_OUnionE__1_decl,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_Datatype__Universe_Ousum_decl,type,
c_Datatype__Universe_Ousum: $i > $i > $i > $i > $i ).
thf(c_Main_OusumE__2_decl,type,
c_Main_OusumE__2: $i > $i > $i > $i > $i ).
thf(c_Main_OusumE__1_decl,type,
c_Main_OusumE__1: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_OFinites_decl,type,
c_Finite__Set_OFinites: $i ).
thf(c_SetInterval_OgreaterThanAtMost_decl,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastAtMost_decl,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_Main_OconverseE__1_decl,type,
c_Main_OconverseE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OconverseE__2_decl,type,
c_Main_OconverseE__2: $i > $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastLessThan_decl,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_Pow_decl,type,
c_Pow: $i > $i > $i ).
thf(c_Main_Oin__listsI__1_decl,type,
c_Main_Oin__listsI__1: $i > $i > $i > $i ).
thf(c_Datatype_Oo2s_decl,type,
c_Datatype_Oo2s: $i > $i > $i ).
thf(c_Datatype__Universe_Ouprod_decl,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__1_decl,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_decl,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_inter_decl,type,
c_inter: $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Orel__compE__1_decl,type,
c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__3_decl,type,
c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__1_decl,type,
c_Main_OdprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__3_decl,type,
c_Main_OdprodE__3: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Ofinite__Union__1_decl,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Main_OdiagE__1_decl,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_Main_OdprodE__2_decl,type,
c_Main_OdprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OdprodE__4_decl,type,
c_Main_OdprodE__4: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__2_decl,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThanLessThan_decl,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Main_OIdE__1_decl,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Inter_decl,type,
c_Inter: $i > $i > $i ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Main_OInterI__1_decl,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Main_ODomainE__1_decl,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i > $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( C @ A ) ) ) )
= B ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_IntDef_Oint @ A )
= B ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Suc @ A )
= B ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i > $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ ( E @ ( D @ ( B @ A ) ) ) )
= C ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
= B ) ) ) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_1) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(29,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff1_0) ).
thf(358,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(359,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[358]) ).
thf(360,plain,
! [A: $i] :
( ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[359]) ).
thf(27,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff1_0) ).
thf(353,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(354,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[353]) ).
thf(355,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[354]) ).
thf(77,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
thf(471,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(83,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1__iff1_0) ).
thf(480,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(481,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[480]) ).
thf(5278,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[471,481]) ).
thf(5279,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[5278]) ).
thf(5325,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[5279]) ).
thf(5342,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_Suc @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[5325]) ).
thf(5560,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,5342]) ).
thf(5561,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5560]) ).
thf(5562,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[5561:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(6401,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[5562]) ).
thf(69,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2__iff1_0) ).
thf(456,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(457,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[456]) ).
thf(9266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6401,457]) ).
thf(9267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9266]) ).
thf(9321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
!= D )
| ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9267]) ).
thf(9340,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( C @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9321]) ).
thf(56794,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( D @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,9340]) ).
thf(56795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( D @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[56794]) ).
thf(56796,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[56795:[bind(A,$thf( tc_nat @ ( tc_nat @ ( I @ ( K @ c_Suc @ c_plus ) ) @ ( E @ c_plus ) ) )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( E ))]]) ).
thf(56880,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[56796]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff2_0) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(413,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
= A ),
inference(lifteq,[status(thm)],[412]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq__iff1_0) ).
thf(348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
inference(cnf,[status(esa)],[348]) ).
thf(350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( D @ ( A @ c_append ) ) ) ) ),
inference(lifteq,[status(thm)],[349]) ).
thf(351,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[350]) ).
thf(352,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( A @ sk2 ) ) )
= B ),
inference(cnf,[status(esa)],[351]) ).
thf(5126,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( A @ sk2 ) ) )
= B ),
inference(lifteq,[status(thm)],[352]) ).
thf(5135,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
!= ( E @ ( D @ ( C @ c_append ) ) ) )
| ( ( A @ ( E @ ( C @ sk2 ) ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[413,5126]) ).
thf(5136,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_List_Olist_ONil @ sk2 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[5135:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_List_Olist_ONil )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(75,axiom,
tc_nat @ class_Nat_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(468,plain,
tc_nat @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(73,axiom,
tc_bool @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).
thf(465,plain,
tc_bool @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
thf(469,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(470,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(cnf,[status(esa)],[469]) ).
thf(33107,plain,
! [A: $i] :
( ( ( tc_bool @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[465,470]) ).
thf(33108,plain,
! [A: $i] :
( ( ( tc_bool @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[33107]) ).
thf(33109,plain,
tc_bool @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[33108:[bind(A,$thf( tc_bool ))]]) ).
thf(33217,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[33109,470]) ).
thf(33218,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[33217]) ).
thf(33219,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[33218:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption ))]]) ).
thf(33340,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33219]) ).
thf(33341,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33340:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq__iff1_0) ).
thf(555,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(82,axiom,
tc_IntDef_Oint @ class_Nat_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(479,plain,
tc_IntDef_Oint @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(4692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[471,457]) ).
thf(4693,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[4692]) ).
thf(4728,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[4693]) ).
thf(4755,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[4728]) ).
thf(6179,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,4755]) ).
thf(6180,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[6179]) ).
thf(6181,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[6180:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).
thf(6313,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[6181]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_0) ).
thf(414,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(415,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[414]) ).
thf(16365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6313,415]) ).
thf(16366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[16365]) ).
thf(16367,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[16366:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( H @ c_Suc @ ( E @ c_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(16501,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[16367]) ).
thf(55,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff1_0) ).
thf(420,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(421,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(cnf,[status(esa)],[420]) ).
thf(422,plain,
! [A: $i] :
( ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[421]) ).
thf(33,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(371,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(266,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(879,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(197,axiom,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__not__finite_0) ).
thf(735,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(736,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[735]) ).
thf(1447,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,736]) ).
thf(1448,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1447]) ).
thf(1453,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_UNIV )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[1448]) ).
thf(1458,plain,
c_Finite__Set_OFinites != c_UNIV,
inference(simp,[status(thm)],[1453]) ).
thf(7043,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,1458]) ).
thf(7044,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7043:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(8401,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
| ( c_UNIV != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,7044]) ).
thf(8402,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[8401]) ).
thf(8449,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[8402]) ).
thf(8457,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ( c_UNIV != c_0 ) ),
inference(simp,[status(thm)],[8449]) ).
thf(19099,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,8457]) ).
thf(19100,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19099]) ).
thf(19101,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[19100:[bind(A,$thf( c_UNIV ))]]) ).
thf(25,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_1) ).
thf(345,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(346,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(cnf,[status(esa)],[345]) ).
thf(347,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(lifteq,[status(thm)],[346]) ).
thf(17,axiom,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0__iff1_0) ).
thf(325,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(326,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[325]) ).
thf(9158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6313,326]) ).
thf(9159,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[9158]) ).
thf(9169,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[9159]) ).
thf(9180,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9169]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff2_0) ).
thf(893,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(150,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(636,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff1_0) ).
thf(541,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(542,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[541]) ).
thf(62782,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[542,326]) ).
thf(62783,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[62782]) ).
thf(62784,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[62783:[bind(A,$thf( A )),bind(B,$thf( c_0 )),bind(C,$thf( A ))]]) ).
thf(63050,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,62784]) ).
thf(63051,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[63050]) ).
thf(63134,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than )
| ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[63051]) ).
thf(63199,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( A @ c_Pair ) ) ) @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than ),
inference(simp,[status(thm)],[63134]) ).
thf(56,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff1_0) ).
thf(423,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(424,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(cnf,[status(esa)],[423]) ).
thf(425,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) )
| ( A = c_0 ) ),
inference(lifteq,[status(thm)],[424]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff2_0) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[309]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[310]) ).
thf(166,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(680,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(133,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(598,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(599,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[598]) ).
thf(2158,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[680,599]) ).
thf(2159,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[2158]) ).
thf(2170,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[2159]) ).
thf(2175,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(simp,[status(thm)],[2170]) ).
thf(2178,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ c_Suc ) )
| ( c_List_Olist_ONil != C )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,2175]) ).
thf(2179,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil != B )
| ( tc_nat @ ( A @ tc_List_Olist @ ( B @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[2178:[bind(A,$thf( D @ c_Suc )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(2182,plain,
! [A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[2179]) ).
thf(4708,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2182,457]) ).
thf(4709,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[4708]) ).
thf(4729,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[4709]) ).
thf(4756,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[4729]) ).
thf(5622,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,4756]) ).
thf(5623,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( C @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[5622]) ).
thf(5624,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[5623:[bind(A,$thf( tc_nat @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( D @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( D ))]]) ).
thf(6421,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[5624]) ).
thf(12764,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6421,326]) ).
thf(12765,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[12764]) ).
thf(12783,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[12765]) ).
thf(12829,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[12783]) ).
thf(22657,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( B @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,12829]) ).
thf(22658,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( B @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[22657]) ).
thf(22659,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[22658:[bind(A,$thf( tc_nat @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( J ))]]) ).
thf(23194,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[22659]) ).
thf(100,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff1_0) ).
thf(517,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(518,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[517]) ).
thf(3,negated_conjecture,
t_a @ ( v_X @ ( v_x @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(297,plain,
t_a @ ( v_X @ ( v_x @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(289,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(925,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(926,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[925]) ).
thf(1273,plain,
! [B: $i,A: $i] :
( ( ( t_a @ ( v_X @ ( v_x @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,926]) ).
thf(1274,plain,
! [B: $i,A: $i] :
( ( t_a @ ( v_X @ ( v_x @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1273]) ).
thf(1277,plain,
! [B: $i,A: $i] :
( ( t_a != B )
| ( c_emptyset != v_X )
| ( v_x != A ) ),
inference(simp,[status(thm)],[1274]) ).
thf(1279,plain,
c_emptyset != v_X,
inference(simp,[status(thm)],[1277]) ).
thf(5571,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != v_X )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,1279]) ).
thf(5572,plain,
( ( c_0 != v_X )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5571:[bind(A,$thf( c_emptyset ))]]) ).
thf(6897,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_X ) ),
inference(paramod_ordered,[status(thm)],[5572,599]) ).
thf(6898,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6897]) ).
thf(6921,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_emptyset != A )
| ( c_0 != A )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6898]) ).
thf(6930,plain,
( ( c_emptyset != c_0 )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6921]) ).
thf(6949,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ( A != v_X )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,6930]) ).
thf(6950,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != v_X )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[6949:[]]) ).
thf(6954,plain,
( ( c_emptyset != c_0 )
| ( tc_nat @ ( v_X @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[6950]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff__iff2_0) ).
thf(666,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff2_0) ).
thf(305,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(306,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
= c_0 ),
inference(lifteq,[status(thm)],[305]) ).
thf(1287,plain,
! [B: $i,A: $i] :
( ( A != c_emptyset )
| ( c_List_Olist_ONil != v_X )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,1279]) ).
thf(1288,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_X )
| ( tc_nat @ ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1287:[bind(A,$thf( c_emptyset ))]]) ).
thf(1289,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_X )
| ( tc_nat @ ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1288]) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != v_X ) ),
inference(paramod_ordered,[status(thm)],[1289,326]) ).
thf(1307,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ( c_List_Olist_ONil != v_X ) ),
inference(simp,[status(thm)],[1306]) ).
thf(1309,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) )
!= c_0 )
| ( c_0 != B )
| ( c_List_Olist_ONil != v_X ) ),
inference(simp,[status(thm)],[1307]) ).
thf(1316,plain,
! [A: $i] :
( ( ( A @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) )
!= c_0 )
| ( c_List_Olist_ONil != v_X ) ),
inference(simp,[status(thm)],[1309]) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ( c_List_Olist_ONil != v_X ) ),
inference(paramod_ordered,[status(thm)],[306,1316]) ).
thf(1377,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( c_emptyset @ c_Nat_Osize ) ) )
| ( c_List_Olist_ONil != v_X ) ),
inference(simp,[status(thm)],[1376]) ).
thf(1378,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist )
!= ( B @ tc_List_Olist ) )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_X ) ),
inference(simp,[status(thm)],[1377]) ).
thf(1498,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_X ) ),
inference(simp,[status(thm)],[1378]) ).
thf(1513,plain,
( ( c_emptyset != c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_X ) ),
inference(simp,[status(thm)],[1498]) ).
thf(6141,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_X )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,1513]) ).
thf(6142,plain,
( ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_X )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[6141:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(683,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(33213,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33109]) ).
thf(33214,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33213:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption ))]]) ).
thf(4710,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[680,457]) ).
thf(4711,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[4710]) ).
thf(4731,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= C )
| ( A
!= ( tc_nat @ ( C @ ( B @ c_plus ) ) ) ) ),
inference(simp,[status(thm)],[4711]) ).
thf(4758,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc )
!= B ),
inference(simp,[status(thm)],[4731]) ).
thf(4985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( C @ c_plus ) ) ) )
| ( ( c_List_Olist_ONil @ c_Suc )
!= D )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,4758]) ).
thf(4986,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ c_Suc )
!= C )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4985:[bind(A,$thf( tc_nat @ ( F @ ( E @ c_plus ) ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(5003,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[4986]) ).
thf(11700,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5003,326]) ).
thf(11701,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[11700]) ).
thf(11720,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[11701]) ).
thf(11755,plain,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[11720]) ).
thf(22811,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( C @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,11755]) ).
thf(22812,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( C @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[22811]) ).
thf(22813,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[22812:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( F @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( F ))]]) ).
thf(23240,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[22813]) ).
thf(33346,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[33219,470]) ).
thf(33347,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[33346]) ).
thf(33348,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[33347:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(33759,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[33348,470]) ).
thf(33760,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[33759]) ).
thf(33761,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[33760:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(33956,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[33761,470]) ).
thf(33957,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[33956]) ).
thf(33958,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[33957:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(34562,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[33958,470]) ).
thf(34563,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[34562]) ).
thf(34564,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[34563:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(34827,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[34564,470]) ).
thf(34828,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[34827]) ).
thf(34829,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[34828:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(9254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6401,481]) ).
thf(9255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9254]) ).
thf(9318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9255]) ).
thf(9337,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9318]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).
thf(449,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_1) ).
thf(379,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(292,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(931,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(4555,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[931,736]) ).
thf(4556,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[4555]) ).
thf(4572,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4556]) ).
thf(4592,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[4572]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_0) ).
thf(861,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(103,axiom,
tc_IntDef_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(523,plain,
tc_IntDef_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex__iff1_0) ).
thf(582,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(9521,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( v_X @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_emptyset != c_0 ) ),
inference(paramod_ordered,[status(thm)],[6954,457]) ).
thf(9522,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( v_X @ ( c_0 @ c_less ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9521]) ).
thf(9562,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B != v_X )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9522]) ).
thf(9573,plain,
! [A: $i] :
( ( ( tc_nat @ ( v_X @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9562]) ).
thf(195,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
thf(730,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(5298,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[680,481]) ).
thf(5299,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[5298]) ).
thf(5317,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ c_Suc )
!= B )
| ( A
!= ( tc_nat @ ( C @ ( B @ c_plus ) ) ) ) ),
inference(simp,[status(thm)],[5299]) ).
thf(5334,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_Suc )
!= A ),
inference(simp,[status(thm)],[5317]) ).
thf(10270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_Suc ) )
| ( c_List_Olist_ONil != C )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,5334]) ).
thf(10271,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil != B )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[10270:[bind(A,$thf( tc_nat @ ( G @ ( F @ c_plus ) ) @ c_Suc )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( G ))]]) ).
thf(10304,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[10271]) ).
thf(13635,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10304,599]) ).
thf(13636,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[13635]) ).
thf(13679,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= C )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[13636]) ).
thf(13725,plain,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[13679]) ).
thf(21425,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,13725]) ).
thf(21426,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[21425]) ).
thf(21427,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[21426:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( H @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( H ))]]) ).
thf(23483,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[21427]) ).
thf(115,axiom,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
thf(547,plain,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(33093,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[547,470]) ).
thf(33094,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[33093]) ).
thf(33095,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[33094:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(33166,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[33095,470]) ).
thf(33167,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[33166]) ).
thf(33168,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[33167:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption ))]]) ).
thf(33276,plain,
! [A: $i] :
( ( A != tc_Product__Type_Ounit )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33168]) ).
thf(33277,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33276:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(249,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(844,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(6,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ ( v_Y @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( v_Z @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( A @ ( v_X @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(295,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ ( v_Y @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( v_Z @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( A @ ( v_X @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(300,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ ( v_Y @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( v_Z @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( A @ ( v_X @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[295]) ).
thf(2620,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ ( v_Y @ c_lessequals ) ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( C @ ( v_Z @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( C @ ( v_X @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[844,300]) ).
thf(2621,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ ( v_Y @ c_lessequals ) ) ) )
| ~ ( t_a @ tc_set @ ( C @ ( v_Z @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( C @ ( v_X @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2620]) ).
thf(2622,plain,
( ~ ( t_a @ tc_set @ ( v_Y @ ( v_Z @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( v_Y @ ( v_X @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[2621:[bind(A,$thf( v_Y )),bind(B,$thf( t_a )),bind(C,$thf( v_Y ))]]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
thf(741,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(10266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( C @ c_plus ) ) ) )
| ( ( c_List_Olist_ONil @ c_Suc )
!= C )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,5334]) ).
thf(10267,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Olist_ONil @ c_Suc )
!= B )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[10266:[bind(A,$thf( tc_nat @ ( F @ ( E @ c_plus ) ) )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(10302,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[10267]) ).
thf(13374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10302,599]) ).
thf(13375,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[13374]) ).
thf(13416,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )
!= C )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[13375]) ).
thf(13462,plain,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[13416]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff2_0) ).
thf(440,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff__iff1_0) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(510,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[509]) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) ) ),
inference(lifteq,[status(thm)],[510]) ).
thf(39,axiom,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff2_0) ).
thf(385,plain,
! [A: $i] :
( c_List_Olist_ONil
= ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,negated_conjecture,
~ ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(293,plain,
~ ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(299,plain,
~ ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[293]) ).
thf(1449,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,299]) ).
thf(1450,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[1449]) ).
thf(1451,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( c_UNIV != v_Y )
| ( A != v_x ) ),
inference(simp,[status(thm)],[1450]) ).
thf(1456,plain,
c_UNIV != v_Y,
inference(simp,[status(thm)],[1451]) ).
thf(5738,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != v_Y )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,1456]) ).
thf(5739,plain,
( ( c_0 != v_Y )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5738:[bind(A,$thf( c_UNIV ))]]) ).
thf(8553,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_Y ) ),
inference(paramod_ordered,[status(thm)],[5739,599]) ).
thf(8554,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[8553]) ).
thf(8579,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_UNIV != A )
| ( c_0 != A )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[8554]) ).
thf(8584,plain,
( ( c_UNIV != c_0 )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[8579]) ).
thf(8606,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ( A != v_Y )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,8584]) ).
thf(8607,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != v_Y )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[8606:[]]) ).
thf(8622,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( v_Y @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[8607]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff__iff1_0) ).
thf(498,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(499,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[498]) ).
thf(500,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) ) ),
inference(lifteq,[status(thm)],[499]) ).
thf(9305,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6401,326]) ).
thf(9306,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[9305]) ).
thf(9316,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
!= c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[9306]) ).
thf(9335,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9316]) ).
thf(19862,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,9335]) ).
thf(19863,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19862]) ).
thf(19864,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[19863:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( E )),bind(C,$thf( G ))]]) ).
thf(20312,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[19864]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff1_0) ).
thf(472,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(119,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(560,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(561,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[560]) ).
thf(70815,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[561,62784]) ).
thf(70816,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[70815]) ).
thf(70817,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( A @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[70816:[bind(A,$thf( c_0 )),bind(B,$thf( c_Wellfounded__Relations_Oless__than )),bind(C,$thf( G )),bind(D,$thf( tc_nat )),bind(E,$thf( tc_nat )),bind(F,$thf( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ ( G @ c_Main_OImageE__1 ) ) ) ) ))]]) ).
thf(70918,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( A @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ),
inference(simp,[status(thm)],[70817]) ).
thf(71027,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,70918]) ).
thf(71028,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) ),
inference(simp,[status(thm)],[71027]) ).
thf(71151,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( tc_nat @ ( tc_nat @ ( C @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= c_UNIV )
| ( A != c_0 ) ),
inference(simp,[status(thm)],[71028]) ).
thf(71221,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[71151]) ).
thf(176,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(698,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(4989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_Suc ) )
| ( c_List_Olist_ONil != D )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,4758]) ).
thf(4990,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Olist_ONil != C )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[4989:[bind(A,$thf( tc_nat @ ( G @ ( F @ c_plus ) ) @ c_Suc )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( G ))]]) ).
thf(5005,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[4990]) ).
thf(5296,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2182,481]) ).
thf(5297,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[5296]) ).
thf(5321,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[5297]) ).
thf(5338,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[5321]) ).
thf(21255,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,5338]) ).
thf(21256,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[21255]) ).
thf(21257,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[21256:[bind(A,$thf( tc_nat @ ( E @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( E ))]]) ).
thf(23423,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[21257]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(338,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(339,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[338]) ).
thf(340,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[339]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex__iff1_0) ).
thf(670,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(9119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6313,457]) ).
thf(9120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9119]) ).
thf(9173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
!= D )
| ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9120]) ).
thf(9184,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( C @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9173]) ).
thf(106,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty__iff1_0) ).
thf(528,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(529,plain,
c_UNIV != c_emptyset,
inference(polarity_switch,[status(thm)],[528]) ).
thf(530,plain,
c_UNIV != c_emptyset,
inference(lifteq,[status(thm)],[529]) ).
thf(18591,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,530]) ).
thf(18592,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[18591:[bind(A,$thf( c_UNIV ))]]) ).
thf(99,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
thf(516,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(54152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[516,926]) ).
thf(54153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[54152]) ).
thf(54216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ tc_prod ) )
!= D )
| ( c_Relation_OId != c_emptyset )
| ( ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) )
!= C ) ),
inference(simp,[status(thm)],[54153]) ).
thf(54228,plain,
c_Relation_OId != c_emptyset,
inference(simp,[status(thm)],[54216]) ).
thf(54275,plain,
! [A: $i] :
( ( A != c_Relation_OId )
| ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,54228]) ).
thf(54276,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_Relation_OId @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[54275:[bind(A,$thf( c_Relation_OId ))]]) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,523]) ).
thf(1048,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1047:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(1137,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1048]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq__iff1_0) ).
thf(550,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(48,axiom,
! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
thf(406,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff2_0) ).
thf(463,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(464,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(cnf,[status(esa)],[463]) ).
thf(31784,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( B @ c_Divides_Oop_Advd ) ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( C @ c_uminus ) @ ( B @ c_Divides_Oop_Advd ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,464]) ).
thf(31785,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( B @ c_Divides_Oop_Advd ) ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( C @ c_uminus ) @ ( B @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[31784]) ).
thf(31786,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[31785:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( c_0 ))]]) ).
thf(32067,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
| ~ $true
| ( B = c_0 ) ),
inference(paramod_ordered,[status(thm)],[31786,422]) ).
thf(32068,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( B @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
| ( B = c_0 ) ),
inference(simp,[status(thm)],[32067]) ).
thf(32069,plain,
( ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) )
= c_0 ),
inference(pattern_uni,[status(thm)],[32068:[bind(A,$thf( c_0 )),bind(B,$thf( tc_IntDef_Oint @ ( c_0 @ c_uminus ) ))]]) ).
thf(17874,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,13462]) ).
thf(17875,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[17874]) ).
thf(17876,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[17875:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( G @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(20352,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[17876]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
thf(715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff1_0) ).
thf(747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff1_0) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( C @ ( A @ c_Datatype_Ooption_OSome ) ) )
| ~ ( C @ ( C @ ( B @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(18498,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != v_Y )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,1456]) ).
thf(18499,plain,
( ( c_0 != v_Y )
| ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[18498:[bind(A,$thf( c_UNIV ))]]) ).
thf(4,negated_conjecture,
~ ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(298,plain,
~ ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(301,plain,
~ ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[298]) ).
thf(1441,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,301]) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[1441]) ).
thf(1454,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( c_UNIV != v_Z )
| ( A != v_x ) ),
inference(simp,[status(thm)],[1442]) ).
thf(1459,plain,
c_UNIV != v_Z,
inference(simp,[status(thm)],[1454]) ).
thf(1466,plain,
! [B: $i,A: $i] :
( ( A != c_UNIV )
| ( c_List_Olist_ONil != v_Z )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,1459]) ).
thf(1467,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_Z )
| ( tc_nat @ ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1466:[bind(A,$thf( c_UNIV ))]]) ).
thf(1468,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_Z )
| ( tc_nat @ ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1467]) ).
thf(2338,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != v_Z ) ),
inference(paramod_ordered,[status(thm)],[1468,599]) ).
thf(2339,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ( c_List_Olist_ONil != v_Z ) ),
inference(simp,[status(thm)],[2338]) ).
thf(2358,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) )
!= B )
| ( c_0 != B )
| ( c_List_Olist_ONil != v_Z ) ),
inference(simp,[status(thm)],[2339]) ).
thf(2369,plain,
! [A: $i] :
( ( ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) )
!= c_0 )
| ( c_List_Olist_ONil != v_Z ) ),
inference(simp,[status(thm)],[2358]) ).
thf(2429,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ( c_List_Olist_ONil != v_Z ) ),
inference(paramod_ordered,[status(thm)],[306,2369]) ).
thf(2430,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) ) )
| ( c_List_Olist_ONil != v_Z ) ),
inference(simp,[status(thm)],[2429]) ).
thf(2441,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist )
!= ( B @ tc_List_Olist ) )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_Z ) ),
inference(simp,[status(thm)],[2430]) ).
thf(4364,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_Z ) ),
inference(simp,[status(thm)],[2441]) ).
thf(4404,plain,
( ( c_UNIV != c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_Z ) ),
inference(simp,[status(thm)],[4364]) ).
thf(6137,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Z )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,4404]) ).
thf(6138,plain,
( ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Z )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[6137:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff2_0) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(320,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff1_0) ).
thf(436,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(8525,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_Y ) ),
inference(paramod_ordered,[status(thm)],[5739,481]) ).
thf(8526,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[8525]) ).
thf(8578,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_UNIV )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[8526]) ).
thf(8583,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_UNIV @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[8578]) ).
thf(242,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(829,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).
thf(404,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(33278,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[33168,470]) ).
thf(33279,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[33278]) ).
thf(33280,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[33279:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(33510,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33280]) ).
thf(33511,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33510:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption ))]]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
thf(898,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_sum ) @ ( D @ ( C @ ( E @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInl ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff1_0) ).
thf(709,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(88,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff1_0) ).
thf(492,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(493,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[492]) ).
thf(62718,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ $true
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[542,599]) ).
thf(62719,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( A @ c_less ) ) )
!= ( tc_nat @ ( C @ ( C @ c_less ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[62718]) ).
thf(62720,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[62719:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(62836,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[62720]) ).
thf(64364,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( F @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[493,62836]) ).
thf(64365,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( F @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[64364]) ).
thf(64366,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[64365:[bind(A,$thf( A )),bind(B,$thf( c_Wellfounded__Relations_Oless__than )),bind(C,$thf( A )),bind(D,$thf( tc_nat )),bind(E,$thf( tc_nat )),bind(F,$thf( A ))]]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(841,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff1_0) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(7733,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Z )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,4404]) ).
thf(7734,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Z )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7733:[bind(A,$thf( c_UNIV ))]]) ).
thf(54269,plain,
! [A: $i] :
( ( A != c_Relation_OId )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,54228]) ).
thf(54270,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Relation_OId @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[54269:[bind(A,$thf( c_Relation_OId ))]]) ).
thf(54964,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Relation_OId @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,54270]) ).
thf(54965,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Relation_OId @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[54964]) ).
thf(55039,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Relation_OId != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[54965]) ).
thf(55063,plain,
( ( c_Relation_OId != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[55039]) ).
thf(55693,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,55063]) ).
thf(55694,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[55693]) ).
thf(55695,plain,
( ( c_Relation_OId != c_0 )
| ~ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[55694:[bind(A,$thf( c_emptyset ))]]) ).
thf(33518,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[33280,470]) ).
thf(33519,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[33518]) ).
thf(33520,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[33519:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(33854,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[33520,470]) ).
thf(33855,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[33854]) ).
thf(33856,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[33855:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(34068,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[33856,470]) ).
thf(34069,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[34068]) ).
thf(34070,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[34069:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(34691,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[34070,470]) ).
thf(34692,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[34691]) ).
thf(34693,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[34692:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(34973,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[34693,470]) ).
thf(34974,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[34973]) ).
thf(34975,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[34974:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(21123,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,1458]) ).
thf(21124,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[21123:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_0) ).
thf(387,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(388,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(cnf,[status(esa)],[387]) ).
thf(389,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[388]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff2_0) ).
thf(570,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(62922,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[518,62784]) ).
thf(62923,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[62922]) ).
thf(62924,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[62923:[bind(A,$thf( c_0 )),bind(B,$thf( B )),bind(C,$thf( tc_nat )),bind(D,$thf( tc_nat )),bind(E,$thf( c_Wellfounded__Relations_Oless__than )),bind(F,$thf( B ))]]) ).
thf(63201,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[62924]) ).
thf(64656,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( F @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[493,63201]) ).
thf(64657,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( F @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[64656]) ).
thf(64658,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[64657:[bind(A,$thf( A )),bind(B,$thf( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) )),bind(C,$thf( c_0 )),bind(D,$thf( tc_nat )),bind(E,$thf( tc_nat )),bind(F,$thf( A ))]]) ).
thf(120,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_1) ).
thf(562,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(563,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(cnf,[status(esa)],[562]) ).
thf(564,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(lifteq,[status(thm)],[563]) ).
thf(565,plain,
? [A: $i > $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ ( E @ ( D @ ( B @ A ) ) ) )
= C ),
inference(detectInverse,[status(thm)],[564]) ).
thf(566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ ( A @ sk8 ) ) ) )
= B ),
inference(cnf,[status(esa)],[565]) ).
thf(72941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ ( D @ ( C @ ( A @ sk8 ) ) ) )
= B ),
inference(lifteq,[status(thm)],[566]) ).
thf(36095,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[34975,470]) ).
thf(36096,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[36095]) ).
thf(36097,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[36096:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff2_0) ).
thf(372,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ ( c_List_Olist_ONil @ c_append ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff__iff2_0) ).
thf(619,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(24,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
thf(344,plain,
! [A: $i] : ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(64738,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,63201]) ).
thf(64739,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[64738]) ).
thf(64847,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) ) )
| ( A
!= ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[64739]) ).
thf(64882,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( A @ ( c_0 @ c_Pair ) ) ) @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) ) ),
inference(simp,[status(thm)],[64847]) ).
thf(22235,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ( A != v_X )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,6930]) ).
thf(22236,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != v_X )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[22235:[]]) ).
thf(23711,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( v_X @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[22236]) ).
thf(1460,plain,
! [B: $i,A: $i] :
( ( A != c_UNIV )
| ( c_List_Olist_ONil != v_Y )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,1456]) ).
thf(1461,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_Y )
| ( tc_nat @ ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1460:[bind(A,$thf( c_UNIV ))]]) ).
thf(1462,plain,
! [A: $i] :
( ( c_List_Olist_ONil != v_Y )
| ( tc_nat @ ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1461]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(503,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(504,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[503]) ).
thf(12433,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5005,326]) ).
thf(12434,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[12433]) ).
thf(12452,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[12434]) ).
thf(12474,plain,
! [B: $i,A: $i] :
( ( A @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[12452]) ).
thf(12536,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,12474]) ).
thf(12537,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[12536]) ).
thf(12538,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[12537:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( G @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(12606,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[12538]) ).
thf(27570,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,12606]) ).
thf(27571,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[27570]) ).
thf(27697,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( B @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ) ),
inference(simp,[status(thm)],[27571]) ).
thf(27725,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[27697]) ).
thf(21030,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,13462]) ).
thf(21031,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[21030]) ).
thf(21032,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[21031:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( G @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(23323,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[21032]) ).
thf(205,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s__iff2_0) ).
thf(751,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Datatype_Ooption_OSome ) @ c_Datatype_Oo2s ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(28,axiom,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0__iff2_0) ).
thf(356,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(357,plain,
( ( tc_nat @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 ),
inference(lifteq,[status(thm)],[356]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_1) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(459,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(cnf,[status(esa)],[458]) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[459]) ).
thf(278,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( E @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
thf(902,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( E @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff2_0) ).
thf(853,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(8565,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_Y )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,5739]) ).
thf(8566,plain,
! [A: $i] :
( ( A != v_Y )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8565:[]]) ).
thf(8590,plain,
( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( v_Y @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[8566]) ).
thf(137,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(606,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(5604,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Orderings_Oorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,606]) ).
thf(5605,plain,
( ( c_0 @ class_Orderings_Oorder )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5604:[bind(A,$thf( tc_nat ))]]) ).
thf(55687,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,55063]) ).
thf(55688,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[55687]) ).
thf(55689,plain,
( ( c_Relation_OId != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[55688:[bind(A,$thf( c_emptyset ))]]) ).
thf(14030,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,13725]) ).
thf(14031,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[14030]) ).
thf(14032,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[14031:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( H @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( H ))]]) ).
thf(14070,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[14032]) ).
thf(28501,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,14070]) ).
thf(28502,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[28501]) ).
thf(28629,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ) ),
inference(simp,[status(thm)],[28502]) ).
thf(28669,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[28629]) ).
thf(6082,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != v_Z )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,1459]) ).
thf(6083,plain,
( ( c_0 != v_Z )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[6082:[bind(A,$thf( c_UNIV ))]]) ).
thf(8977,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_Z ) ),
inference(paramod_ordered,[status(thm)],[6083,481]) ).
thf(8978,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[8977]) ).
thf(9032,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_UNIV )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[8978]) ).
thf(9039,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_UNIV @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[9032]) ).
thf(193,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(728,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(1483,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[728,736]) ).
thf(1484,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1483]) ).
thf(1490,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1484]) ).
thf(1494,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1490]) ).
thf(7073,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != v_X )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,1279]) ).
thf(7074,plain,
( ( c_0 != v_X )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7073:[bind(A,$thf( c_emptyset ))]]) ).
thf(9376,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_X )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,7074]) ).
thf(9377,plain,
! [A: $i] :
( ( A != v_X )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9376:[]]) ).
thf(9420,plain,
( ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) )
| ~ ( tc_nat @ ( c_0 @ ( v_X @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9377]) ).
thf(5836,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_plus ) ) ) )
| ( ( c_0 @ c_Suc )
!= C )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,4758]) ).
thf(5837,plain,
! [B: $i,A: $i] :
( ( ( c_0 @ c_Suc )
!= B )
| ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5836:[bind(A,$thf( tc_nat @ ( E @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(6504,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[5837]) ).
thf(6628,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6504,481]) ).
thf(6629,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[6628]) ).
thf(6688,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= B )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[6629]) ).
thf(6704,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[6688]) ).
thf(11106,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,6704]) ).
thf(11107,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[11106]) ).
thf(11108,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[11107:[bind(A,$thf( tc_nat @ ( E @ ( tc_nat @ ( c_0 @ c_Suc @ ( G @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(11159,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[11108]) ).
thf(16684,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,11159]) ).
thf(16685,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[16684]) ).
thf(16765,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( tc_nat @ ( B @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[16685]) ).
thf(16809,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[16765]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_0) ).
thf(313,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(314,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(cnf,[status(esa)],[313]) ).
thf(315,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(lifteq,[status(thm)],[314]) ).
thf(316,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[315]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(cnf,[status(esa)],[316]) ).
thf(1319,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(lifteq,[status(thm)],[317]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff1_0) ).
thf(870,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(65802,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,64366]) ).
thf(65803,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[65802]) ).
thf(65896,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[65803]) ).
thf(65948,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) ) ),
inference(simp,[status(thm)],[65896]) ).
thf(7124,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,4756]) ).
thf(7125,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7124]) ).
thf(7126,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[7125:[bind(A,$thf( tc_nat @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( D @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( D ))]]) ).
thf(8235,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[7126]) ).
thf(213,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
thf(770,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_sum ) @ ( C @ ( D @ ( B @ ( E @ c_Sum__Type_OPlus ) ) ) @ ( D @ ( C @ ( A @ c_Sum__Type_OInr ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(258,axiom,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(863,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(1396,plain,
! [A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[863,299]) ).
thf(1397,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[1396]) ).
thf(1398,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_Y )
| ( c_emptyset != v_x ) ),
inference(simp,[status(thm)],[1397]) ).
thf(53,axiom,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left__iff2_0) ).
thf(416,plain,
tc_IntDef_Oint @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1469,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[728,301]) ).
thf(1470,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[1469]) ).
thf(1489,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_Z )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= v_x ) ),
inference(simp,[status(thm)],[1470]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
thf(474,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_List_Oset ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[474]) ).
thf(33516,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33280]) ).
thf(33517,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33516:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[442]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2__iff1_0) ).
thf(376,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(7676,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != v_Z )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,1459]) ).
thf(7677,plain,
( ( c_0 != v_Z )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7676:[bind(A,$thf( c_UNIV ))]]) ).
thf(85,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
thf(485,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ( A != tc_nat )
| ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,468]) ).
thf(1046,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1045:[bind(A,$thf( tc_nat ))]]) ).
thf(1136,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1046]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(834,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(13506,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,13462]) ).
thf(13507,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[13506]) ).
thf(13508,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[13507:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( G @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(13543,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[13508]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff2_0) ).
thf(821,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(7167,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_X )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,5572]) ).
thf(7168,plain,
! [A: $i] :
( ( A != v_X )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7167:[]]) ).
thf(7899,plain,
( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( v_X @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7168]) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(cnf,[status(esa)],[550]) ).
thf(552,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_IntDef_Oint )
!= ( B @ c_IntDef_Oint ) ) ),
inference(lifteq,[status(thm)],[551]) ).
thf(553,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_IntDef_Oint @ A )
= B ),
inference(detectInverse,[status(thm)],[552]) ).
thf(554,plain,
! [A: $i] :
( ( A @ c_IntDef_Oint @ sk6 )
= A ),
inference(cnf,[status(esa)],[553]) ).
thf(2017,plain,
! [A: $i] :
( ( A @ c_IntDef_Oint @ sk6 )
= A ),
inference(lifteq,[status(thm)],[554]) ).
thf(33753,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33348]) ).
thf(33754,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33753:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption ))]]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff__iff2_0) ).
thf(634,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff2_1) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(391,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[390]) ).
thf(12240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6313,391]) ).
thf(12241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[12240]) ).
thf(12242,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[12241:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( H @ c_Suc @ ( E @ c_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(12313,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[12242]) ).
thf(61674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( D @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12313,599]) ).
thf(61675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( D @ c_less ) ) ) ),
inference(simp,[status(thm)],[61674]) ).
thf(61743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) )
!= D )
| ( c_0 != D ) ),
inference(simp,[status(thm)],[61675]) ).
thf(61788,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[61743]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff__iff1_0) ).
thf(453,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
thf(774,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_List_Oset ) @ ( C @ ( A @ ( B @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(147,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty__iff1_0) ).
thf(631,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(632,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[631]) ).
thf(6911,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_X ) ),
inference(paramod_ordered,[status(thm)],[5572,632]) ).
thf(6912,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ) )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6911]) ).
thf(6923,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( c_emptyset != c_emptyset )
| ( c_0 != A )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6912]) ).
thf(6932,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6923]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv__iff1_1) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(6673,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6504,326]) ).
thf(6674,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[6673]) ).
thf(6686,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != B ) ),
inference(simp,[status(thm)],[6674]) ).
thf(6702,plain,
! [A: $i] :
( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[6686]) ).
thf(58,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq__iff2_0) ).
thf(428,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(2085,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != v_Y ) ),
inference(paramod_ordered,[status(thm)],[1462,326]) ).
thf(2086,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( B @ c_less ) ) ) )
| ( c_List_Olist_ONil != v_Y ) ),
inference(simp,[status(thm)],[2085]) ).
thf(2102,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) )
!= c_0 )
| ( c_0 != B )
| ( c_List_Olist_ONil != v_Y ) ),
inference(simp,[status(thm)],[2086]) ).
thf(2112,plain,
! [A: $i] :
( ( ( A @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) )
!= c_0 )
| ( c_List_Olist_ONil != v_Y ) ),
inference(simp,[status(thm)],[2102]) ).
thf(2129,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ( c_List_Olist_ONil != v_Y ) ),
inference(paramod_ordered,[status(thm)],[306,2112]) ).
thf(2130,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) )
!= ( B @ tc_List_Olist @ ( c_UNIV @ c_Nat_Osize ) ) )
| ( c_List_Olist_ONil != v_Y ) ),
inference(simp,[status(thm)],[2129]) ).
thf(2141,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_List_Olist )
!= ( B @ tc_List_Olist ) )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_Y ) ),
inference(simp,[status(thm)],[2130]) ).
thf(3082,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_Y ) ),
inference(simp,[status(thm)],[2141]) ).
thf(3110,plain,
( ( c_UNIV != c_List_Olist_ONil )
| ( c_List_Olist_ONil != v_Y ) ),
inference(simp,[status(thm)],[3082]) ).
thf(5955,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Y )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,3110]) ).
thf(5956,plain,
( ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Y )
| ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5955:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(13220,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Y ) ),
inference(paramod_ordered,[status(thm)],[5956,326]) ).
thf(13221,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[13220]) ).
thf(13233,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_List_Olist_ONil != c_0 )
| ( c_0 != A )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[13221]) ).
thf(13248,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[13233]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_1) ).
thf(602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(33272,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33168]) ).
thf(33273,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33272:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(692,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterD_0) ).
thf(866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(6641,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6504,457]) ).
thf(6642,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( C @ ( B @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[6641]) ).
thf(6685,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( C @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[6642]) ).
thf(6701,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_plus ) ) @ ( B @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[6685]) ).
thf(11009,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,6701]) ).
thf(11010,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[11009]) ).
thf(11011,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[11010:[bind(A,$thf( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( G @ c_plus ) ) @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).
thf(11045,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[11011]) ).
thf(15689,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ ( B @ c_plus ) ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,11045]) ).
thf(15690,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ ( B @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[15689]) ).
thf(15772,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( C @ c_plus ) ) @ ( B @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[15690]) ).
thf(15799,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_0 @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[15772]) ).
thf(2220,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( c_emptyset @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2182,632]) ).
thf(2221,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( c_emptyset @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[2220]) ).
thf(2240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= tc_nat )
| ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= c_emptyset )
| ( c_0 != B ) ),
inference(simp,[status(thm)],[2221]) ).
thf(2242,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[2240]) ).
thf(64654,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,63201]) ).
thf(64655,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[64654]) ).
thf(64835,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) )
!= c_UNIV )
| ( A
!= ( tc_nat @ ( tc_nat @ ( C @ ( c_0 @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[64655]) ).
thf(64875,plain,
( ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[64835]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[526]) ).
thf(11,axiom,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(312,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oneq0__conv__iff2_0) ).
thf(307,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(9021,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_Z ) ),
inference(paramod_ordered,[status(thm)],[6083,326]) ).
thf(9022,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[9021]) ).
thf(9031,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_UNIV != c_0 )
| ( c_0 != A )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[9022]) ).
thf(9038,plain,
( ( c_UNIV != c_0 )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[9031]) ).
thf(23039,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ( A != v_Z )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,9038]) ).
thf(23040,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != v_Z )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[23039:[]]) ).
thf(23304,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( v_Z @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23040]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
thf(451,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(452,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(cnf,[status(esa)],[451]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
thf(920,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff2_0) ).
thf(678,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(158,axiom,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff1_0) ).
thf(661,plain,
! [A: $i] :
( ( A = c_0 )
| ~ ( tc_nat @ ( c_0 @ c_Suc @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff2_0) ).
thf(545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( A @ ( D @ c_append ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[545]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_0) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(cnf,[status(esa)],[532]) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(lifteq,[status(thm)],[533]) ).
thf(227,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
thf(798,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( C @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(97,axiom,
tc_nat @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(512,plain,
tc_nat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(62,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(439,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(18306,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,12474]) ).
thf(18307,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[18306]) ).
thf(18308,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[18307:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( G @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(20500,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[18308]) ).
thf(16188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6401,415]) ).
thf(16189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[16188]) ).
thf(16190,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[16189:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( F @ ( H @ c_Suc @ c_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(16467,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[16190]) ).
thf(62082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( D @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16467,599]) ).
thf(62083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( D @ ( D @ c_less ) ) ) ),
inference(simp,[status(thm)],[62082]) ).
thf(62145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) )
!= D )
| ( c_0 != D ) ),
inference(simp,[status(thm)],[62083]) ).
thf(62196,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[62145]) ).
thf(380,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(cnf,[status(esa)],[379]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ( B = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(lifteq,[status(thm)],[380]) ).
thf(5486,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Orderings_Oord )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,523]) ).
thf(5487,plain,
( ( c_0 @ class_Orderings_Oord )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5486:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(31,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject__iff1_1) ).
thf(364,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(365,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(cnf,[status(esa)],[364]) ).
thf(366,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(lifteq,[status(thm)],[365]) ).
thf(9003,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_Z )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,6083]) ).
thf(9004,plain,
! [A: $i] :
( ( A != v_Z )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9003:[]]) ).
thf(9041,plain,
( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( v_Z @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9004]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(910,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff1_0) ).
thf(825,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(217,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(778,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(367,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[366]) ).
thf(368,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( A @ sk3 ) ) )
= B ),
inference(cnf,[status(esa)],[367]) ).
thf(9075,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( C @ ( A @ sk3 ) ) )
= B ),
inference(lifteq,[status(thm)],[368]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2__iff1_0) ).
thf(407,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq__iff1_0) ).
thf(429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(54271,plain,
! [A: $i] :
( ( A != c_Relation_OId )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,54228]) ).
thf(54272,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_Relation_OId @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[54271:[bind(A,$thf( c_Relation_OId ))]]) ).
thf(194,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
thf(729,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_IntDef_Oint @ c_uminus ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(11810,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( C @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,11755]) ).
thf(11811,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( C @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[11810]) ).
thf(11812,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[11811:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( F @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( F ))]]) ).
thf(11860,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[11812]) ).
thf(17361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,11860]) ).
thf(17362,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[17361]) ).
thf(17446,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( C @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( B @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ) ),
inference(simp,[status(thm)],[17362]) ).
thf(17467,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[17446]) ).
thf(10691,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,5338]) ).
thf(10692,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[10691]) ).
thf(10693,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[10692:[bind(A,$thf( tc_nat @ ( E @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( E ))]]) ).
thf(10714,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[10693]) ).
thf(14181,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10714,326]) ).
thf(14182,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[14181]) ).
thf(14204,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )
!= c_0 )
| ( c_0 != C ) ),
inference(simp,[status(thm)],[14182]) ).
thf(14249,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[14204]) ).
thf(18534,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( C @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,14249]) ).
thf(18535,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( C @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[18534]) ).
thf(18536,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[18535:[bind(A,$thf( tc_nat @ ( E @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )),bind(B,$thf( E )),bind(C,$thf( J ))]]) ).
thf(19950,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[18536]) ).
thf(20,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv__iff1_0) ).
thf(332,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(333,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(cnf,[status(esa)],[332]) ).
thf(334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( C @ ( c_List_Olist_ONil @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_append ) ) )
!= ( C @ ( C @ ( c_List_Olist_ONil @ ( E @ c_List_Olist_OCons ) ) @ ( D @ c_append ) ) ) ) ),
inference(lifteq,[status(thm)],[333]) ).
thf(33162,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33095]) ).
thf(33163,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33162:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption ))]]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv__iff1_0) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(237,axiom,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(820,plain,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_0) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1485,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[728,299]) ).
thf(1486,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[1485]) ).
thf(1487,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_Y )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= v_x ) ),
inference(simp,[status(thm)],[1486]) ).
thf(7315,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,530]) ).
thf(7316,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7315:[bind(A,$thf( c_UNIV ))]]) ).
thf(10315,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,7316]) ).
thf(10316,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[10315]) ).
thf(10364,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[10316]) ).
thf(10380,plain,
( ( c_UNIV != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[10364]) ).
thf(19019,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,10380]) ).
thf(19020,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19019]) ).
thf(19021,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[19020:[bind(A,$thf( c_emptyset ))]]) ).
thf(235,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
thf(815,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1__iff1_0) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv__iff1_1) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(62984,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,62784]) ).
thf(62985,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[62984]) ).
thf(63137,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( c_UNIV != c_Wellfounded__Relations_Oless__than )
| ( A
!= ( tc_nat @ ( tc_nat @ ( c_0 @ ( C @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[62985]) ).
thf(63200,plain,
c_UNIV != c_Wellfounded__Relations_Oless__than,
inference(simp,[status(thm)],[63137]) ).
thf(63231,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,63200]) ).
thf(63232,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[63231:[bind(A,$thf( c_UNIV ))]]) ).
thf(16,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(324,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(403,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(cnf,[status(esa)],[402]) ).
thf(14679,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) )
!= ( C @ ( B @ c_Wellfounded__Recursion_Owf ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[324,403]) ).
thf(14680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) )
!= ( C @ ( B @ c_Wellfounded__Recursion_Owf ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(simp,[status(thm)],[14679]) ).
thf(14681,plain,
! [A: $i] : ( A @ tc_List_Olist @ ( A @ ( c_emptyset @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ),
inference(pattern_uni,[status(thm)],[14680:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( A ))]]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff2_0) ).
thf(889,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(71,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(461,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
thf(916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff1_0) ).
thf(466,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(467,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) ) ),
inference(cnf,[status(esa)],[466]) ).
thf(251,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
thf(847,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(483,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[482]) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[483]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero__iff1_0) ).
thf(341,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(342,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(polarity_switch,[status(thm)],[341]) ).
thf(343,plain,
! [A: $i] :
( ( A @ c_Suc )
!= c_0 ),
inference(lifteq,[status(thm)],[342]) ).
thf(21723,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,343]) ).
thf(21724,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[21723]) ).
thf(21725,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[21724:[bind(A,$thf( C @ c_Suc )),bind(B,$thf( C ))]]) ).
thf(23577,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[21725]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject__iff1_0) ).
thf(626,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(627,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(cnf,[status(esa)],[626]) ).
thf(628,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Datatype_Ooption_OSome ) )
!= ( B @ ( C @ c_Datatype_Ooption_OSome ) ) ) ),
inference(lifteq,[status(thm)],[627]) ).
thf(629,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Datatype_Ooption_OSome ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[628]) ).
thf(630,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk12 ) )
= A ),
inference(cnf,[status(esa)],[629]) ).
thf(58523,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Datatype_Ooption_OSome ) @ ( B @ sk12 ) )
= A ),
inference(lifteq,[status(thm)],[630]) ).
thf(173,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(694,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(2641,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[694,736]) ).
thf(2642,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[2641]) ).
thf(2660,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2642]) ).
thf(2663,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[2660]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0) ).
thf(434,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(435,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(cnf,[status(esa)],[434]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff1_0) ).
thf(521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(cnf,[status(esa)],[521]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff2_0) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(5657,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_HOL_Ominus )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,439]) ).
thf(5658,plain,
( ( c_0 @ class_HOL_Ominus )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5657:[bind(A,$thf( tc_nat ))]]) ).
thf(63235,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,63200]) ).
thf(63236,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[63235:[bind(A,$thf( c_UNIV ))]]) ).
thf(1392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[863,926]) ).
thf(1393,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[1392]) ).
thf(1399,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set )
!= C )
| ( c_Finite__Set_OFinites != c_emptyset )
| ( c_emptyset != B ) ),
inference(simp,[status(thm)],[1393]) ).
thf(1402,plain,
c_Finite__Set_OFinites != c_emptyset,
inference(simp,[status(thm)],[1399]) ).
thf(101,axiom,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff2_0) ).
thf(519,plain,
! [A: $i] :
( c_emptyset
= ( A @ ( c_List_Olist_ONil @ c_List_Oset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(142,axiom,
tc_IntDef_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(615,plain,
tc_IntDef_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(191,axiom,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(725,plain,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(8613,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ( A != v_Y )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,8584]) ).
thf(8614,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != v_Y )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[8613:[]]) ).
thf(8619,plain,
( ( c_UNIV != c_0 )
| ( tc_nat @ ( v_Y @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[8614]) ).
thf(111,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
thf(540,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(29029,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Orderings_Oorder )
!= ( A @ class_Orderings_Oorder ) )
| ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[615,452]) ).
thf(29030,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Orderings_Oorder )
!= ( A @ class_Orderings_Oorder ) )
| ~ ( A @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[29029]) ).
thf(29031,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[29030:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(29225,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ ( A @ c_less ) ) ),
inference(simp,[status(thm)],[29031]) ).
thf(29317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[540,29225]) ).
thf(29318,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[29317]) ).
thf(29440,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_IntDef_Oint )
| ( ( B @ c_IntDef_Oint )
!= C )
| ( ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) )
!= C ) ),
inference(simp,[status(thm)],[29318]) ).
thf(29448,plain,
! [B: $i,A: $i] :
( ( B @ c_IntDef_Oint )
!= ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) ) ),
inference(simp,[status(thm)],[29440]) ).
thf(131,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
thf(593,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( E @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_Sum__Type_OInr ) ) ) )
| ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_Sum__Type_OInl ) ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(2217,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2182,599]) ).
thf(2218,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[2217]) ).
thf(2238,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= B )
| ( c_0 != B ) ),
inference(simp,[status(thm)],[2218]) ).
thf(2252,plain,
! [A: $i] :
( ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[2238]) ).
thf(22217,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,2252]) ).
thf(22218,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[22217]) ).
thf(22219,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[22218:[bind(A,$thf( F @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( F ))]]) ).
thf(23708,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[22219]) ).
thf(7254,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,1402]) ).
thf(7255,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7254:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(9853,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,7255]) ).
thf(9854,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_Finite__Set_OFinites @ c_lessequals ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9853]) ).
thf(9905,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9854]) ).
thf(9916,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9905]) ).
thf(22320,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,9916]) ).
thf(22321,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[22320]) ).
thf(22322,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[22321:[bind(A,$thf( c_emptyset ))]]) ).
thf(67161,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,64658]) ).
thf(67162,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[67161]) ).
thf(67368,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) )
!= c_UNIV )
| ( A != C ) ),
inference(simp,[status(thm)],[67162]) ).
thf(67418,plain,
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[67368]) ).
thf(140,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(610,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(5957,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Y )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,3110]) ).
thf(5958,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Y )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5957:[bind(A,$thf( c_UNIV ))]]) ).
thf(13862,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Y ) ),
inference(paramod_ordered,[status(thm)],[5958,326]) ).
thf(13863,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Y ) ),
inference(simp,[status(thm)],[13862]) ).
thf(13878,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_UNIV != c_0 )
| ( c_0 != A )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Y ) ),
inference(simp,[status(thm)],[13863]) ).
thf(13899,plain,
( ( c_UNIV != c_0 )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Y ) ),
inference(simp,[status(thm)],[13878]) ).
thf(56491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( D @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,9184]) ).
thf(56492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( D @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[56491]) ).
thf(56493,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[56492:[bind(A,$thf( tc_nat @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ ( E @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( E ))]]) ).
thf(56561,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[56493]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(884,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(19602,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( C @ c_plus ) ) @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,11755]) ).
thf(19603,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( C @ c_plus ) ) @ c_Nat_Osize ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19602]) ).
thf(19604,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[19603:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( F @ c_plus ) ) @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( F ))]]) ).
thf(20248,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ c_Suc @ ( A @ c_plus ) ) @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[19604]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff2_0) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
= A ),
inference(lifteq,[status(thm)],[318]) ).
thf(430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
inference(cnf,[status(esa)],[429]) ).
thf(431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= ( C @ ( B @ ( D @ c_append ) ) ) ) ),
inference(lifteq,[status(thm)],[430]) ).
thf(432,plain,
? [A: $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ c_append ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[431]) ).
thf(433,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( B @ sk4 ) ) )
= A ),
inference(cnf,[status(esa)],[432]) ).
thf(24481,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_append ) ) @ ( C @ ( B @ sk4 ) ) )
= A ),
inference(lifteq,[status(thm)],[433]) ).
thf(24504,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
!= ( E @ ( D @ ( C @ c_append ) ) ) )
| ( ( A @ ( E @ ( D @ sk4 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[319,24481]) ).
thf(24505,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_List_Olist_ONil @ sk4 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[24504:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_List_Olist_ONil )),bind(E,$thf( B ))]]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr__iff1_0) ).
thf(537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(80,axiom,
tc_IntDef_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(476,plain,
tc_IntDef_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq__iff1_0) ).
thf(642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(151,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(637,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(18015,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != v_X )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,1279]) ).
thf(18016,plain,
( ( c_0 != v_X )
| ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[18015:[bind(A,$thf( c_emptyset ))]]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty__iff1_0) ).
thf(487,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(488,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
inference(cnf,[status(esa)],[487]) ).
thf(489,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ ( A @ c_List_Oset ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[488]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(837,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff__iff1_0) ).
thf(647,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff2_0) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(156,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(654,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(32082,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( B @ c_Divides_Oop_Advd ) ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( C @ c_uminus ) @ ( B @ c_Divides_Oop_Advd ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31786,464]) ).
thf(32083,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( C @ ( B @ c_Divides_Oop_Advd ) ) ) )
| ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( C @ c_uminus ) @ ( B @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[32082]) ).
thf(32084,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[32083:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( tc_IntDef_Oint @ ( c_0 @ c_uminus ) ))]]) ).
thf(32265,plain,
! [A: $i] : ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( c_0 @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(rewrite,[status(thm)],[32084,32069]) ).
thf(7737,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_X )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,1513]) ).
thf(7738,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_X )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7737:[bind(A,$thf( c_emptyset ))]]) ).
thf(189,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff2_0) ).
thf(721,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(12093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6401,391]) ).
thf(12094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( c_0 @ c_less ) ) ) )
| ( tc_nat @ ( tc_nat @ ( C @ ( D @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[12093]) ).
thf(12095,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[12094:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( tc_nat @ ( F @ ( H @ c_Suc @ c_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(12301,plain,
! [C: $i,B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ),
inference(simp,[status(thm)],[12095]) ).
thf(61006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( D @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12301,326]) ).
thf(61007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( D @ c_less ) ) ) ),
inference(simp,[status(thm)],[61006]) ).
thf(61028,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != D ) ),
inference(simp,[status(thm)],[61007]) ).
thf(61093,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ ( A @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[61028]) ).
thf(55705,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,55063]) ).
thf(55706,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Relation_OId != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[55705]) ).
thf(55707,plain,
( ( c_Relation_OId != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[55706:[bind(A,$thf( c_emptyset ))]]) ).
thf(122,axiom,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc0__iff2_0) ).
thf(569,plain,
tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(308,plain,
~ ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[307]) ).
thf(982,plain,
( ( ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[569,308]) ).
thf(983,plain,
( ( tc_nat @ ( c_0 @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[982]) ).
thf(984,plain,
( ( tc_nat != tc_nat )
| ( ( c_0 @ c_Suc )
!= c_0 )
| ( c_0 != c_0 ) ),
inference(simp,[status(thm)],[983]) ).
thf(985,plain,
( ( c_0 @ c_Suc )
!= c_0 ),
inference(simp,[status(thm)],[984]) ).
thf(8551,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_Y )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,5739]) ).
thf(8552,plain,
! [A: $i] :
( ( A != v_Y )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[8551:[]]) ).
thf(8587,plain,
( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( c_0 @ ( v_Y @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[8552]) ).
thf(2,negated_conjecture,
t_a @ tc_set @ ( v_X @ ( v_Z @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(296,plain,
t_a @ tc_set @ ( v_X @ ( v_Z @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5822,plain,
! [A: $i] :
( ( A
!= ( t_a @ tc_set ) )
| ( c_0 @ ( v_X @ ( v_Z @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,296]) ).
thf(5823,plain,
( ( c_0 @ ( v_X @ ( v_Z @ c_lessequals ) ) )
| ( tc_nat @ ( t_a @ tc_set @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5822:[bind(A,$thf( t_a @ tc_set ))]]) ).
thf(224,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(792,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(230,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(805,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl__iff1_0) ).
thf(506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
inference(polarity_switch,[status(thm)],[506]) ).
thf(508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInl ) ) ) ),
inference(lifteq,[status(thm)],[507]) ).
thf(9017,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_Z )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,6083]) ).
thf(9018,plain,
! [A: $i] :
( ( A != v_Z )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9017:[]]) ).
thf(9044,plain,
( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( v_Z @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9018]) ).
thf(211,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(765,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(16143,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_X ) ),
inference(paramod_ordered,[status(thm)],[6142,326]) ).
thf(16144,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[16143]) ).
thf(16156,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_List_Olist_ONil != c_0 )
| ( c_0 != A )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[16144]) ).
thf(16169,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[16156]) ).
thf(6889,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_X ) ),
inference(paramod_ordered,[status(thm)],[5572,457]) ).
thf(6890,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6889]) ).
thf(6922,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B != c_emptyset )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6890]) ).
thf(6931,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6922]) ).
thf(148,axiom,
! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_1) ).
thf(633,plain,
! [B: $i,A: $i] : ( B @ ( A @ tc_fun ) @ class_Nat_Opower ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(35932,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[34829,470]) ).
thf(35933,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[35932]) ).
thf(35934,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[35933:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(36265,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[35934,470]) ).
thf(36266,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[36265]) ).
thf(36267,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[36266:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(44941,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[36267,470]) ).
thf(44942,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[44941]) ).
thf(44943,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[44942:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(794,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq__iff2_0) ).
thf(586,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(239,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(824,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1972,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[824,736]) ).
thf(1973,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1972]) ).
thf(1991,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1973]) ).
thf(1996,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1991]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(271,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(888,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(32232,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( ( c_0 @ ( c_0 @ c_uminus ) )
= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,32069]) ).
thf(32233,plain,
( ( ( c_0 @ ( c_0 @ c_uminus ) )
= c_0 )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[32232:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(19566,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ( A != v_Y )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,8584]) ).
thf(19567,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != v_Y )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[19566:[]]) ).
thf(20236,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_IntDef_Oint @ ( v_Y @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19567]) ).
thf(5137,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) )
!= ( E @ ( D @ ( C @ c_append ) ) ) )
| ( ( A @ ( E @ ( C @ sk2 ) ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[319,5126]) ).
thf(5138,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ sk2 ) ) )
= c_List_Olist_ONil ),
inference(pattern_uni,[status(thm)],[5137:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( c_List_Olist_ONil )),bind(E,$thf( B ))]]) ).
thf(7511,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Y )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,3110]) ).
thf(7512,plain,
( ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Y )
| ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7511:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(9107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6313,481]) ).
thf(9108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( C @ ( tc_nat @ ( D @ ( C @ c_plus ) ) @ c_less ) ) ) ),
inference(simp,[status(thm)],[9107]) ).
thf(9170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) )
!= C )
| ( ( tc_nat @ ( D @ ( C @ c_plus ) ) )
!= c_0 ) ),
inference(simp,[status(thm)],[9108]) ).
thf(9181,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[9170]) ).
thf(65,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_0) ).
thf(444,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(9065,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ( A != v_Z )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,9038]) ).
thf(9066,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != v_Z )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9065:[]]) ).
thf(9072,plain,
( ( c_UNIV != c_0 )
| ( tc_nat @ ( v_Z @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9066]) ).
thf(7062,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,5342]) ).
thf(7063,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_Suc @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7062]) ).
thf(7064,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[7063:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( E ))]]) ).
thf(8215,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[7064]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2__iff1_0) ).
thf(513,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( c_emptyset
!= ( B @ ( A @ c_List_Oset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1073,plain,
! [B: $i,A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_List_Olist_ONil @ class_Orderings_Olinorder )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,476]) ).
thf(1074,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Olinorder )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1073:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(1146,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Olinorder )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1074]) ).
thf(5450,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,312]) ).
thf(5451,plain,
( ( tc_nat @ ( c_0 @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5450:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff1_1) ).
thf(856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(62986,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[493,62784]) ).
thf(62987,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( c_0 @ ( F @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[62986]) ).
thf(62988,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[62987:[bind(A,$thf( c_0 )),bind(B,$thf( c_Wellfounded__Relations_Oless__than )),bind(C,$thf( C )),bind(D,$thf( tc_nat )),bind(E,$thf( tc_nat )),bind(F,$thf( C ))]]) ).
thf(63152,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ),
inference(simp,[status(thm)],[62988]) ).
thf(63383,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,63152]) ).
thf(63384,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) ),
inference(simp,[status(thm)],[63383]) ).
thf(63488,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) ) )
| ( A != c_0 ) ),
inference(simp,[status(thm)],[63384]) ).
thf(63489,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) ) ),
inference(simp,[status(thm)],[63488]) ).
thf(107,axiom,
tc_IntDef_Oint @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(531,plain,
tc_IntDef_Oint @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(6000,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_HOL_Ominus )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,531]) ).
thf(6001,plain,
( ( c_0 @ class_HOL_Ominus )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[6000:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse__iff1_0) ).
thf(745,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff__iff1_0) ).
thf(689,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(94,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(505,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(5978,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Orderings_Olinorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,505]) ).
thf(5979,plain,
( ( c_0 @ class_Orderings_Olinorder )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5978:[bind(A,$thf( tc_nat ))]]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0__iff1_0) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( B @ ( c_0 @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_less ) ) ) ),
inference(cnf,[status(esa)],[374]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
thf(733,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( A @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_Oin__listsI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(56633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,9337]) ).
thf(56634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[56633]) ).
thf(56635,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[56634:[bind(A,$thf( tc_nat @ ( F @ ( tc_nat @ ( I @ ( K @ c_Suc @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( F ))]]) ).
thf(56714,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[56635]) ).
thf(8898,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,8457]) ).
thf(8899,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[8898]) ).
thf(8900,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[8899:[bind(A,$thf( c_UNIV ))]]) ).
thf(7735,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_X )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,1513]) ).
thf(7736,plain,
( ( c_emptyset != c_List_Olist_ONil )
| ( c_0 != v_X )
| ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7735:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(45472,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[44943,470]) ).
thf(45473,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[45472]) ).
thf(45474,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[45473:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(47478,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[45474,470]) ).
thf(47479,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[47478]) ).
thf(47480,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[47479:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(48101,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[47480,470]) ).
thf(48102,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[48101]) ).
thf(48103,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[48102:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(49204,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[48103,470]) ).
thf(49205,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[49204]) ).
thf(49206,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[49205:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert__iff2_0) ).
thf(584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(6139,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Z )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,4404]) ).
thf(6140,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Z )
| ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[6139:[bind(A,$thf( c_UNIV ))]]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H__iff2_0) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(56480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( D @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,9184]) ).
thf(56481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( D @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[56480]) ).
thf(56482,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[56481:[bind(A,$thf( tc_nat @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ ( E @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( E ))]]) ).
thf(56556,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[56482]) ).
thf(22701,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != v_Z )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,1459]) ).
thf(22702,plain,
( ( c_0 != v_Z )
| ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[22701:[bind(A,$thf( c_UNIV ))]]) ).
thf(214,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(772,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(56666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,9337]) ).
thf(56667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[56666]) ).
thf(56668,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[56667:[bind(A,$thf( tc_nat @ ( F @ ( tc_nat @ ( I @ ( K @ c_Suc @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( F ))]]) ).
thf(56729,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[56668]) ).
thf(18257,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,13725]) ).
thf(18258,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( C @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[18257]) ).
thf(18259,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[18258:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( H @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( H ))]]) ).
thf(20486,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[18259]) ).
thf(33164,plain,
! [A: $i] :
( ( A != tc_Product__Type_Ounit )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33095]) ).
thf(33165,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33164:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(7770,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,4755]) ).
thf(7771,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7770]) ).
thf(7772,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[7771:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).
thf(8124,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[7772]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert__iff2_0) ).
thf(743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(264,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
thf(875,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( E @ ( A @ ( C @ c_Main_OPlusE__2 ) ) ) @ c_in ) ) )
| ( D @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OPlusE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_sum ) @ ( E @ ( D @ ( C @ ( B @ c_Sum__Type_OPlus ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(7509,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ( A != v_X )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,6930]) ).
thf(7510,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != v_X )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7509:[]]) ).
thf(8027,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( v_X @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7510]) ).
thf(71080,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,70918]) ).
thf(71081,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( C @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) ),
inference(simp,[status(thm)],[71080]) ).
thf(71157,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( C @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) ) )
| ( A != c_0 ) ),
inference(simp,[status(thm)],[71081]) ).
thf(71226,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) ) ),
inference(simp,[status(thm)],[71157]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff__iff2_0) ).
thf(787,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff1_0) ).
thf(335,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(33342,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33219]) ).
thf(33343,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33342:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption ))]]) ).
thf(445,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(cnf,[status(esa)],[444]) ).
thf(446,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(lifteq,[status(thm)],[445]) ).
thf(447,plain,
? [A: $i > $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( C @ A ) ) ) )
= B ),
inference(detectInverse,[status(thm)],[446]) ).
thf(448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( B @ sk5 ) ) ) )
= A ),
inference(cnf,[status(esa)],[447]) ).
thf(27507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( B @ sk5 ) ) ) )
= A ),
inference(lifteq,[status(thm)],[448]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(672,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1055,plain,
! [B: $i,A: $i] :
( ( A != tc_nat )
| ( c_List_Olist_ONil @ class_Orderings_Oorder )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,606]) ).
thf(1056,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oorder )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1055:[bind(A,$thf( tc_nat ))]]) ).
thf(1139,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oorder )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1056]) ).
thf(38,axiom,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc__iff1_0) ).
thf(382,plain,
! [A: $i] :
( c_0
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(33514,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33280]) ).
thf(33515,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33514:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(63312,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[879,63152]) ).
thf(63313,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) @ ( c_0 @ c_in ) ) ) ),
inference(simp,[status(thm)],[63312]) ).
thf(63477,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( C @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= c_UNIV )
| ( A != c_0 ) ),
inference(simp,[status(thm)],[63313]) ).
thf(63571,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_OImage ) ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[63477]) ).
thf(6909,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_X )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,5572]) ).
thf(6910,plain,
! [A: $i] :
( ( A != v_X )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[6909:[]]) ).
thf(6937,plain,
( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
| ( tc_nat @ ( v_X @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[6910]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1) ).
thf(604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(6143,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_X )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,1513]) ).
thf(6144,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_X )
| ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[6143:[bind(A,$thf( c_emptyset ))]]) ).
thf(19119,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,9916]) ).
thf(19120,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19119]) ).
thf(19121,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[19120:[bind(A,$thf( c_emptyset ))]]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
thf(784,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(cnf,[status(esa)],[417]) ).
thf(419,plain,
! [B: $i,A: $i] :
( ( A = c_0 )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 ) ),
inference(lifteq,[status(thm)],[418]) ).
thf(1521,plain,
! [B: $i,A: $i] :
( ( c_List_Olist_ONil != c_List_Olist_ONil )
| ( c_emptyset != c_List_Olist_ONil )
| ( A != v_X )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,1513]) ).
thf(1522,plain,
! [B: $i,A: $i] :
( ( c_emptyset != c_List_Olist_ONil )
| ( A != v_X )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1521:[]]) ).
thf(1524,plain,
! [A: $i] :
( ( c_emptyset != c_List_Olist_ONil )
| ( tc_nat @ ( A @ tc_List_Olist @ ( v_X @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1522]) ).
thf(1069,plain,
! [B: $i,A: $i] :
( ( A != tc_nat )
| ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,512]) ).
thf(1070,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1069:[bind(A,$thf( tc_nat ))]]) ).
thf(1144,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Orderings_Oord )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1070]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1__iff1_0) ).
thf(616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn0 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(9513,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( v_X @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_emptyset != c_0 ) ),
inference(paramod_ordered,[status(thm)],[6954,481]) ).
thf(9514,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( v_X @ ( c_0 @ c_less ) ) ) )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9513]) ).
thf(9564,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != v_X )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9514]) ).
thf(9575,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( v_X @ c_plus ) ) )
!= c_0 )
| ( c_emptyset != c_0 ) ),
inference(simp,[status(thm)],[9564]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(58586,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,301]) ).
thf(58587,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[58586]) ).
thf(58664,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= v_Z )
| ( A != v_x ) ),
inference(simp,[status(thm)],[58587]) ).
thf(58694,plain,
( ( t_a @ ( c_emptyset @ ( v_x @ c_insert ) ) )
!= v_Z ),
inference(simp,[status(thm)],[58664]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(7513,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Y )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,3110]) ).
thf(7514,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Y )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7513:[bind(A,$thf( c_UNIV ))]]) ).
thf(21771,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,530]) ).
thf(21772,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[21771:[bind(A,$thf( c_UNIV ))]]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff__iff1_0) ).
thf(567,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono__iff1_0) ).
thf(737,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(24498,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) )
!= ( E @ ( D @ ( C @ c_append ) ) ) )
| ( ( A @ ( E @ ( D @ sk4 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[413,24481]) ).
thf(24499,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ sk4 ) ) )
= c_List_Olist_ONil ),
inference(pattern_uni,[status(thm)],[24498:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_List_Olist_ONil )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(267,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(880,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq__iff1_0) ).
thf(649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInl ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(81,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
thf(477,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0__iff1_0) ).
thf(494,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(15,axiom,
tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff__iff2_0) ).
thf(323,plain,
tc_nat @ ( c_0 @ ( c_0 @ c_Divides_Oop_Advd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(5655,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Orderings_Oord )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,512]) ).
thf(5656,plain,
( ( c_0 @ class_Orderings_Oord )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5655:[bind(A,$thf( tc_nat ))]]) ).
thf(462,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[461]) ).
thf(233,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(811,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(5729,plain,
! [A: $i] :
( ( A != tc_Product__Type_Ounit )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,547]) ).
thf(5730,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5729:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq__iff1_0) ).
thf(621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(19815,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ( A != v_Z )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,9038]) ).
thf(19816,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != v_Z )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[19815:[]]) ).
thf(20298,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_IntDef_Oint @ ( v_Z @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19816]) ).
thf(36445,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[36097,470]) ).
thf(36446,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[36445]) ).
thf(36447,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[36446:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(45202,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[36447,470]) ).
thf(45203,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[45202]) ).
thf(45204,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[45203:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(46987,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[45204,470]) ).
thf(46988,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[46987]) ).
thf(46989,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[46988:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(520,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Oset ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[519]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(58633,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,299]) ).
thf(58634,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[58633]) ).
thf(58671,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= v_Y )
| ( A != v_x ) ),
inference(simp,[status(thm)],[58634]) ).
thf(58704,plain,
( ( t_a @ ( c_emptyset @ ( v_x @ c_insert ) ) )
!= v_Y ),
inference(simp,[status(thm)],[58671]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0) ).
thf(668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(33755,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33348]) ).
thf(33756,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33755:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv__iff1_0) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff__iff1_0) ).
thf(780,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(454,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[453]) ).
thf(455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) ) ),
inference(lifteq,[status(thm)],[454]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0) ).
thf(608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(14906,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( A @ ( c_emptyset @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( C @ ( B @ c_Wellfounded__Recursion_Owf ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14681,403]) ).
thf(14907,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_List_Olist @ ( A @ ( c_emptyset @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( C @ ( B @ c_Wellfounded__Recursion_Owf ) ) )
| ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(simp,[status(thm)],[14906]) ).
thf(14908,plain,
! [A: $i] : ( A @ tc_List_Olist @ tc_List_Olist @ ( A @ tc_List_Olist @ ( A @ ( c_emptyset @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ),
inference(pattern_uni,[status(thm)],[14907:[bind(A,$thf( F )),bind(B,$thf( F @ ( c_emptyset @ c_List_Olex ) )),bind(C,$thf( F @ tc_List_Olist ))]]) ).
thf(14947,plain,
! [A: $i] : ( A @ tc_List_Olist @ tc_List_Olist @ ( A @ tc_List_Olist @ ( A @ ( c_emptyset @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ),
inference(simp,[status(thm)],[14908]) ).
thf(282,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(912,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(169,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
thf(685,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_Datatype__Universe_OIn0 ) ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff__iff1_0) ).
thf(768,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(241,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(827,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(2030,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( c_emptyset @ ( B @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[471,632]) ).
thf(2031,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( c_0 @ c_less ) ) )
!= ( C @ tc_set @ ( c_emptyset @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[2030]) ).
thf(2044,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= tc_nat )
| ( ( A @ c_Suc )
!= c_emptyset )
| ( c_0 != B ) ),
inference(simp,[status(thm)],[2031]) ).
thf(2051,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( ( A @ c_Suc )
!= c_emptyset ) ),
inference(simp,[status(thm)],[2044]) ).
thf(174,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(695,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(33274,plain,
! [A: $i] :
( ( A
!= ( tc_Product__Type_Ounit @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33168]) ).
thf(33275,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33274:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption ))]]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff2_0) ).
thf(868,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(56644,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,9337]) ).
thf(56645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[56644]) ).
thf(56646,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[56645:[bind(A,$thf( tc_nat @ ( F @ ( tc_nat @ ( I @ ( K @ c_Suc @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( F ))]]) ).
thf(56719,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[56646]) ).
thf(14676,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[312,403]) ).
thf(14677,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(simp,[status(thm)],[14676]) ).
thf(14678,plain,
tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ),
inference(pattern_uni,[status(thm)],[14677:[bind(A,$thf( c_Wellfounded__Relations_Oless__than )),bind(B,$thf( tc_nat ))]]) ).
thf(14722,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14678,403]) ).
thf(14723,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(simp,[status(thm)],[14722]) ).
thf(14724,plain,
tc_nat @ tc_List_Olist @ tc_List_Olist @ ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ),
inference(pattern_uni,[status(thm)],[14723:[bind(A,$thf( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) )),bind(B,$thf( tc_nat @ tc_List_Olist ))]]) ).
thf(14798,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_List_Olist @ tc_List_Olist @ ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14724,403]) ).
thf(14799,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_List_Olist @ tc_List_Olist @ ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
!= ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) )
| ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(simp,[status(thm)],[14798]) ).
thf(14800,plain,
tc_nat @ tc_List_Olist @ tc_List_Olist @ tc_List_Olist @ ( tc_nat @ tc_List_Olist @ tc_List_Olist @ ( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_List_Olex ) @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ),
inference(pattern_uni,[status(thm)],[14799:[bind(A,$thf( tc_nat @ tc_List_Olist @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_List_Olex ) @ c_List_Olex ) )),bind(B,$thf( tc_nat @ tc_List_Olist @ tc_List_Olist ))]]) ).
thf(1,negated_conjecture,
t_a @ tc_set @ ( v_X @ ( v_Y @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(294,plain,
t_a @ tc_set @ ( v_X @ ( v_Y @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6211,plain,
! [A: $i] :
( ( A
!= ( t_a @ tc_set ) )
| ( c_0 @ ( v_X @ ( v_Y @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,294]) ).
thf(6212,plain,
( ( c_0 @ ( v_X @ ( v_Y @ c_lessequals ) ) )
| ( tc_nat @ ( t_a @ tc_set @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[6211:[bind(A,$thf( t_a @ tc_set ))]]) ).
thf(287,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(922,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(5462,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Nat_Opower )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,479]) ).
thf(5463,plain,
( ( c_0 @ class_Nat_Opower )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5462:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(26539,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ tc_set @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 @ ( v_X @ ( v_Z @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[5823,599]) ).
thf(26540,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ tc_set @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 @ ( v_X @ ( v_Z @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[26539]) ).
thf(26578,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( t_a @ tc_set )
!= A )
| ( c_0 != A )
| ( c_0 @ ( v_X @ ( v_Z @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[26540]) ).
thf(26591,plain,
( ( ( t_a @ tc_set )
!= c_0 )
| ( c_0 @ ( v_X @ ( v_Z @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[26578]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2__iff2_0) ).
thf(426,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( A @ ( c_List_Olist_ONil @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(116,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff__iff2_0) ).
thf(548,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(18433,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,1402]) ).
thf(18434,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[18433:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(204,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( E @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
thf(749,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( E @ c_Datatype__Universe_Ousum ) ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(936,plain,
( ( ( t_a @ ( v_Z @ ( v_x @ c_in ) ) )
!= ( t_a @ ( v_X @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,301]) ).
thf(937,plain,
( ( t_a @ ( v_Z @ ( v_x @ c_in ) ) )
!= ( t_a @ ( v_X @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[936]) ).
thf(938,plain,
( ( t_a != t_a )
| ( v_Z != v_X )
| ( v_x != v_x ) ),
inference(simp,[status(thm)],[937]) ).
thf(939,plain,
v_Z != v_X,
inference(simp,[status(thm)],[938]) ).
thf(27188,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ tc_set @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_0 @ ( v_X @ ( v_Y @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6212,599]) ).
thf(27189,plain,
! [A: $i] :
( ( ( tc_nat @ ( t_a @ tc_set @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_0 @ ( v_X @ ( v_Y @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[27188]) ).
thf(27224,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( t_a @ tc_set )
!= A )
| ( c_0 != A )
| ( c_0 @ ( v_X @ ( v_Y @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[27189]) ).
thf(27235,plain,
( ( ( t_a @ tc_set )
!= c_0 )
| ( c_0 @ ( v_X @ ( v_Y @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[27224]) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ( A != tc_nat )
| ( c_List_Olist_ONil @ class_HOL_Ominus )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,439]) ).
thf(1072,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_HOL_Ominus )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1071:[bind(A,$thf( tc_nat ))]]) ).
thf(1145,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_HOL_Ominus )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_nat @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1072]) ).
thf(9493,plain,
! [B: $i,A: $i] :
( ( c_0 != c_0 )
| ( ( B @ tc_set )
!= tc_nat )
| ( A != v_X )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,6932]) ).
thf(9494,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( A != v_X )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9493:[]]) ).
thf(9507,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ~ ( tc_nat @ ( c_0 @ ( v_X @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9494]) ).
thf(473,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(cnf,[status(esa)],[472]) ).
thf(47785,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[46989,470]) ).
thf(47786,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[47785]) ).
thf(47787,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[47786:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(48431,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[47787,470]) ).
thf(48432,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[48431]) ).
thf(48433,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[48432:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(556,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(cnf,[status(esa)],[555]) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(lifteq,[status(thm)],[556]) ).
thf(558,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Suc @ A )
= B ),
inference(detectInverse,[status(thm)],[557]) ).
thf(559,plain,
! [A: $i] :
( ( A @ c_Suc @ sk7 )
= A ),
inference(cnf,[status(esa)],[558]) ).
thf(2054,plain,
! [A: $i] :
( ( A @ c_Suc @ sk7 )
= A ),
inference(lifteq,[status(thm)],[559]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff2_0) ).
thf(490,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_0) ).
thf(675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un__iff2_0) ).
thf(927,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,479]) ).
thf(1039,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1038:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(1134,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Nat_Opower )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_IntDef_Oint @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1039]) ).
thf(1958,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[824,301]) ).
thf(1959,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[1958]) ).
thf(1990,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_Z )
| ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= v_x ) ),
inference(simp,[status(thm)],[1959]) ).
thf(27924,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,13543]) ).
thf(27925,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[27924]) ).
thf(28048,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( ( C @ tc_List_Olist @ ( tc_nat @ ( B @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ) ),
inference(simp,[status(thm)],[27925]) ).
thf(28067,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( tc_nat @ ( A @ ( c_List_Olist_ONil @ c_Suc @ c_plus ) ) @ c_Nat_Osize ) )
!= c_0 ),
inference(simp,[status(thm)],[28048]) ).
thf(90,axiom,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(497,plain,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(11190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[497,926]) ).
thf(11191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[11190]) ).
thf(11221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_List_Olist )
!= D )
| ( ( B @ ( A @ c_List_Olists ) )
!= c_emptyset )
| ( c_List_Olist_ONil != C ) ),
inference(simp,[status(thm)],[11191]) ).
thf(11230,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_List_Olists ) )
!= c_emptyset ),
inference(simp,[status(thm)],[11221]) ).
thf(56513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( D @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,9184]) ).
thf(56514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( D @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[56513]) ).
thf(56515,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[56514:[bind(A,$thf( tc_nat @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ ( E @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( E ))]]) ).
thf(56571,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[56515]) ).
thf(216,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
thf(776,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( B @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(67250,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,64658]) ).
thf(67251,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[67250]) ).
thf(67362,plain,
! [C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[67251]) ).
thf(67412,plain,
! [A: $i] :
( ( tc_nat @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( tc_nat @ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_insert ) ) @ ( tc_nat @ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Oconverse ) ) @ c_Relation_OImage ) ) ) ) ),
inference(simp,[status(thm)],[67362]) ).
thf(263,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
thf(872,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__4 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__3 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__2 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Main_OdprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Odprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(2700,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[695,736]) ).
thf(2701,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[2700]) ).
thf(2718,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2701]) ).
thf(2732,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[2718]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(10390,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,10380]) ).
thf(10391,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[10390]) ).
thf(10392,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[10391:[bind(A,$thf( c_emptyset ))]]) ).
thf(15169,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Z ) ),
inference(paramod_ordered,[status(thm)],[6140,599]) ).
thf(15170,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Z ) ),
inference(simp,[status(thm)],[15169]) ).
thf(15201,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_UNIV != A )
| ( c_0 != A )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Z ) ),
inference(simp,[status(thm)],[15170]) ).
thf(15220,plain,
( ( c_UNIV != c_0 )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_Z ) ),
inference(simp,[status(thm)],[15201]) ).
thf(19034,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_emptyset != c_0 )
| ( A != v_X )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,6930]) ).
thf(19035,plain,
! [A: $i] :
( ( c_emptyset != c_0 )
| ( A != v_X )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[19034:[]]) ).
thf(20080,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_IntDef_Oint @ ( v_X @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19035]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).
thf(524,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(525,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_sum ) @ class_Finite__Set_Ofinite ) ),
inference(cnf,[status(esa)],[524]) ).
thf(5715,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Orderings_Oorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,615]) ).
thf(5716,plain,
( ( c_0 @ class_Orderings_Oorder )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5715:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_1) ).
thf(580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(254,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
thf(855,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_List_Oset ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(55572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,9181]) ).
thf(55573,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[55572]) ).
thf(55574,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[55573:[bind(A,$thf( tc_nat @ ( F @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( F ))]]) ).
thf(55632,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[55574]) ).
thf(180,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
thf(705,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_in ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(17967,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_UNIV != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,1458]) ).
thf(17968,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_IntDef_Oint @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[17967:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(1384,plain,
! [A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[863,301]) ).
thf(1385,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( t_a @ ( v_Z @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[1384]) ).
thf(1400,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_Z )
| ( c_emptyset != v_x ) ),
inference(simp,[status(thm)],[1385]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(707,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(8985,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_Z ) ),
inference(paramod_ordered,[status(thm)],[6083,457]) ).
thf(8986,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[8985]) ).
thf(9030,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B != c_UNIV )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[8986]) ).
thf(9037,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[9030]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv__iff2_0) ).
thf(327,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( c_List_Olist_ONil @ ( A @ c_append ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(18543,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,343]) ).
thf(18544,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[18543]) ).
thf(18545,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[18544:[bind(A,$thf( C @ c_Suc )),bind(B,$thf( C ))]]) ).
thf(19954,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ c_Suc @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[18545]) ).
thf(22775,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ( A != v_Y )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,8584]) ).
thf(22776,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != v_Y )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[22775:[]]) ).
thf(23228,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( v_Y @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[22776]) ).
thf(18294,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ c_plus ) ) ) )
| ( ( c_0 @ c_Suc )
!= B )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,5334]) ).
thf(18295,plain,
! [B: $i,A: $i] :
( ( ( c_0 @ c_Suc )
!= A )
| ~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[18294:[bind(A,$thf( tc_nat @ ( E @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(20496,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[18295]) ).
thf(24297,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,20496]) ).
thf(24298,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) )
!= ( tc_IntDef_Oint @ ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[24297]) ).
thf(24345,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_IntDef_Oint )
| ( ( tc_nat @ ( B @ ( c_0 @ c_Suc @ c_plus ) ) )
!= c_0 )
| ( A != c_0 ) ),
inference(simp,[status(thm)],[24298]) ).
thf(24357,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_Suc @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[24345]) ).
thf(63229,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,63200]) ).
thf(63230,plain,
( ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[63229:[bind(A,$thf( c_UNIV ))]]) ).
thf(68225,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[371,63230]) ).
thf(68226,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_0 @ c_lessequals ) ) )
!= ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[68225]) ).
thf(68299,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_0 )
| ( c_UNIV != c_0 )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[68226]) ).
thf(68314,plain,
( ( c_UNIV != c_0 )
| ( c_Wellfounded__Relations_Oless__than != c_0 ) ),
inference(simp,[status(thm)],[68299]) ).
thf(68350,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,68314]) ).
thf(68351,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[68350]) ).
thf(68352,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_Wellfounded__Relations_Oless__than @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[68351:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_append ) ) ) ) ),
inference(cnf,[status(esa)],[329]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[330]) ).
thf(441,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(cnf,[status(esa)],[440]) ).
thf(186,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(717,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(92,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
thf(501,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(502,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn0 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn0 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[501]) ).
thf(21678,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != v_Y )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,1456]) ).
thf(21679,plain,
( ( c_0 != v_Y )
| ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[21678:[bind(A,$thf( c_UNIV ))]]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(370,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(cnf,[status(esa)],[369]) ).
thf(10677,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,5338]) ).
thf(10678,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[10677]) ).
thf(10679,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[10678:[bind(A,$thf( tc_nat @ ( E @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) )),bind(B,$thf( J )),bind(C,$thf( E ))]]) ).
thf(10739,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[10679]) ).
thf(7495,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,2252]) ).
thf(7496,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7495]) ).
thf(7497,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[7496:[bind(A,$thf( F @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( F ))]]) ).
thf(8024,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[7497]) ).
thf(29080,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ class_Orderings_Oorder )
!= ( B @ class_Orderings_Oorder ) )
| ~ ( B @ ( C @ ( C @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[922,452]) ).
thf(29081,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ class_Orderings_Oorder )
!= ( B @ class_Orderings_Oorder ) )
| ~ ( B @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[29080]) ).
thf(29082,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[29081:[bind(A,$thf( D )),bind(B,$thf( D @ tc_set ))]]) ).
thf(29192,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(simp,[status(thm)],[29082]) ).
thf(22300,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,8457]) ).
thf(22301,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[22300]) ).
thf(22302,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[22301:[bind(A,$thf( c_UNIV ))]]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff__iff1_0) ).
thf(543,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(544,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( B @ ( tc_IntDef_Oint @ ( A @ c_uminus ) @ c_Divides_Oop_Advd ) ) ) ),
inference(cnf,[status(esa)],[543]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff__iff1_0) ).
thf(703,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(157,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq__iff1_1) ).
thf(656,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff__iff1_0) ).
thf(864,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(5452,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,312]) ).
thf(5453,plain,
( ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ) )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5452:[bind(A,$thf( tc_nat ))]]) ).
thf(9928,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,9916]) ).
thf(9929,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9928]) ).
thf(9930,plain,
( ( c_Finite__Set_OFinites != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9929:[bind(A,$thf( c_emptyset ))]]) ).
thf(22220,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,10380]) ).
thf(22221,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[22220]) ).
thf(22222,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[22221:[bind(A,$thf( c_emptyset ))]]) ).
thf(68344,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_UNIV != c_0 )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,68314]) ).
thf(68345,plain,
! [A: $i] :
( ( A != c_Wellfounded__Relations_Oless__than )
| ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[68344]) ).
thf(68346,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( c_Wellfounded__Relations_Oless__than @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[68345:[bind(A,$thf( c_Wellfounded__Relations_Oless__than ))]]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__iff1_0) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(4638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( D @ tc_set @ ( c_emptyset @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[540,632]) ).
thf(4639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( D @ tc_set @ ( c_emptyset @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[4638]) ).
thf(4656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ tc_set )
!= tc_IntDef_Oint )
| ( ( B @ c_IntDef_Oint )
!= c_emptyset )
| ( ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) )
!= C ) ),
inference(simp,[status(thm)],[4639]) ).
thf(4671,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_IntDef_Oint )
| ( ( A @ c_IntDef_Oint )
!= c_emptyset ) ),
inference(simp,[status(thm)],[4656]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(600,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(19016,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,2252]) ).
thf(19017,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19016]) ).
thf(19018,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[19017:[bind(A,$thf( F @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( F ))]]) ).
thf(20077,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[19018]) ).
thf(256,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(859,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff2_0) ).
thf(845,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(55594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,9181]) ).
thf(55595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[55594]) ).
thf(55596,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[55595:[bind(A,$thf( tc_nat @ ( F @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( F ))]]) ).
thf(55642,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[55596]) ).
thf(170,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(688,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(22921,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,4755]) ).
thf(22922,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[22921]) ).
thf(22923,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[22922:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).
thf(23261,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[22923]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(273,axiom,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).
thf(891,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(450,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
inference(cnf,[status(esa)],[449]) ).
thf(19492,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != v_Z )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,1459]) ).
thf(19493,plain,
( ( c_0 != v_Z )
| ~ ( tc_IntDef_Oint @ ( c_UNIV @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[19492:[bind(A,$thf( c_UNIV ))]]) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(polarity_switch,[status(thm)],[361]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[362]) ).
thf(538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
inference(polarity_switch,[status(thm)],[537]) ).
thf(539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Sum__Type_OInl ) ) )
!= ( B @ ( C @ ( D @ c_Sum__Type_OInr ) ) ) ),
inference(lifteq,[status(thm)],[538]) ).
thf(2844,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_X @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ~ $true
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(paramod_ordered,[status(thm)],[1524,599]) ).
thf(2845,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ tc_List_Olist @ ( v_X @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( B @ ( B @ c_less ) ) ) )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2844]) ).
thf(2862,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( A @ tc_List_Olist @ ( v_X @ c_Nat_Osize ) )
!= B )
| ( c_0 != B )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2845]) ).
thf(2870,plain,
! [A: $i] :
( ( ( A @ tc_List_Olist @ ( v_X @ c_Nat_Osize ) )
!= c_0 )
| ( c_emptyset != c_List_Olist_ONil ) ),
inference(simp,[status(thm)],[2862]) ).
thf(7731,plain,
! [A: $i] :
( ( A != c_List_Olist_ONil )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Z )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,4404]) ).
thf(7732,plain,
( ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Z )
| ~ ( tc_nat @ ( c_0 @ ( c_List_Olist_ONil @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7731:[bind(A,$thf( c_List_Olist_ONil ))]]) ).
thf(68968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( D @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16501,326]) ).
thf(68969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( D @ c_less ) ) ) ),
inference(simp,[status(thm)],[68968]) ).
thf(68995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) )
!= c_0 )
| ( c_0 != D ) ),
inference(simp,[status(thm)],[68969]) ).
thf(69005,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) )
!= c_0 ),
inference(simp,[status(thm)],[68995]) ).
thf(234,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(813,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
inference(cnf,[status(esa)],[399]) ).
thf(401,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= A ) ),
inference(lifteq,[status(thm)],[400]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(786,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq__iff1_0) ).
thf(588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_Sum__Type_OInr ) ) )
!= ( C @ ( B @ ( D @ c_Sum__Type_OInr ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(699,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
inference(cnf,[status(esa)],[302]) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) )
!= c_0 ) ),
inference(lifteq,[status(thm)],[303]) ).
thf(21474,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,12474]) ).
thf(21475,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( C @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[21474]) ).
thf(21476,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[21475:[bind(A,$thf( J @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( G @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) )),bind(B,$thf( J )),bind(C,$thf( G ))]]) ).
thf(23497,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ tc_List_Olist @ ( tc_nat @ ( c_List_Olist_ONil @ ( A @ c_plus ) ) @ c_Suc @ c_Nat_Osize ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[21476]) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
inference(cnf,[status(esa)],[376]) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ( ( C @ ( B @ ( A @ c_append ) ) )
!= B ) ),
inference(lifteq,[status(thm)],[377]) ).
thf(9499,plain,
! [B: $i,A: $i] :
( ( c_0 != c_0 )
| ( ( B @ tc_set )
!= tc_nat )
| ( A != v_X )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,6932]) ).
thf(9500,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set )
!= tc_nat )
| ( A != v_X )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9499:[]]) ).
thf(9510,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= tc_nat )
| ( tc_nat @ ( v_X @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9500]) ).
thf(478,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( F @ c_Datatype__Universe_Odsum ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ c_Datatype__Universe_OIn1 ) ) @ ( D @ ( C @ ( A @ c_Datatype__Universe_OIn1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[477]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(549,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[548]) ).
thf(536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[535]) ).
thf(568,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ ( A @ c_Divides_Oop_Advd ) ) )
| ~ ( tc_IntDef_Oint @ ( tc_IntDef_Oint @ ( B @ c_uminus ) @ ( A @ c_Divides_Oop_Advd ) ) ) ),
inference(cnf,[status(esa)],[567]) ).
thf(23086,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,9335]) ).
thf(23087,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ ( C @ c_Suc @ c_plus ) ) ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[23086]) ).
thf(23088,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[23087:[bind(A,$thf( tc_nat @ ( E @ ( G @ c_Suc @ c_plus ) ) )),bind(B,$thf( E )),bind(C,$thf( G ))]]) ).
thf(23330,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_Suc @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[23088]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(929,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(9392,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( A != v_X )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,7074]) ).
thf(9393,plain,
! [A: $i] :
( ( A != v_X )
| ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[9392:[]]) ).
thf(9421,plain,
( ~ ( tc_nat @ ( c_0 @ ( c_emptyset @ c_lessequals ) ) )
| ( tc_nat @ ( v_X @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[9393]) ).
thf(55561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,9181]) ).
thf(55562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( D @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[55561]) ).
thf(55563,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[55562:[bind(A,$thf( tc_nat @ ( F @ ( tc_nat @ ( K @ c_Suc @ ( H @ c_plus ) ) @ c_plus ) ) )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( F ))]]) ).
thf(55627,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_nat @ ( c_0 @ ( tc_nat @ ( A @ ( tc_nat @ ( C @ c_Suc @ ( B @ c_plus ) ) @ c_plus ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[55563]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq__iff1_1) ).
thf(800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(206,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(752,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(58615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,926]) ).
thf(58616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[58615]) ).
thf(58676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_emptyset )
| ( A != C ) ),
inference(simp,[status(thm)],[58616]) ).
thf(58711,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[58676]) ).
thf(4640,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[540,326]) ).
thf(4641,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint @ ( B @ c_IntDef_Oint @ ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[4640]) ).
thf(4655,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_nat )
| ( ( B @ c_IntDef_Oint )
!= c_0 )
| ( ( tc_IntDef_Oint @ ( A @ c_Suc @ c_IntDef_Oint @ c_uminus ) )
!= C ) ),
inference(simp,[status(thm)],[4641]) ).
thf(4670,plain,
! [A: $i] :
( ( tc_IntDef_Oint != tc_nat )
| ( ( A @ c_IntDef_Oint )
!= c_0 ) ),
inference(simp,[status(thm)],[4655]) ).
thf(33215,plain,
! [A: $i] :
( ( A != tc_bool )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33109]) ).
thf(33216,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33215:[bind(A,$thf( tc_bool ))]]) ).
thf(50,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv__iff1_0) ).
thf(410,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(818,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(9058,plain,
! [A: $i] :
( ( c_0 != c_0 )
| ( c_UNIV != c_0 )
| ( A != v_Z )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,9038]) ).
thf(9059,plain,
! [A: $i] :
( ( c_UNIV != c_0 )
| ( A != v_Z )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[9058:[]]) ).
thf(9070,plain,
( ( c_UNIV != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( v_Z @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9059]) ).
thf(33512,plain,
! [A: $i] :
( ( A != tc_Product__Type_Ounit )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33280]) ).
thf(33513,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_Product__Type_Ounit @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33512:[bind(A,$thf( tc_Product__Type_Ounit ))]]) ).
thf(5727,plain,
! [A: $i] :
( ( A != tc_IntDef_Oint )
| ( c_0 @ class_Orderings_Olinorder )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,476]) ).
thf(5728,plain,
( ( c_0 @ class_Orderings_Olinorder )
| ( tc_nat @ ( tc_IntDef_Oint @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5727:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(58370,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[49206,470]) ).
thf(58371,plain,
! [A: $i] :
( ( ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[58370]) ).
thf(58372,plain,
tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[58371:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(17085,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_X ) ),
inference(paramod_ordered,[status(thm)],[6144,599]) ).
thf(17086,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( A @ ( A @ c_less ) ) ) )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_X ) ),
inference(simp,[status(thm)],[17085]) ).
thf(17120,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_emptyset != A )
| ( c_0 != A )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_X ) ),
inference(simp,[status(thm)],[17086]) ).
thf(17140,plain,
( ( c_emptyset != c_0 )
| ( c_List_Olist_ONil != c_0 )
| ( c_List_Olist_ONil != v_X ) ),
inference(simp,[status(thm)],[17120]) ).
thf(405,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite ) ),
inference(cnf,[status(esa)],[404]) ).
thf(58625,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,736]) ).
thf(58626,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[58625]) ).
thf(58674,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ tc_set ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Finite__Set_OFinites )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[58626]) ).
thf(58708,plain,
( ( tc_nat @ tc_set @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[58674]) ).
thf(5476,plain,
! [A: $i] :
( ( A != tc_nat )
| ( c_0 @ class_Nat_Opower )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,468]) ).
thf(5477,plain,
( ( c_0 @ class_Nat_Opower )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5476:[bind(A,$thf( tc_nat ))]]) ).
thf(64419,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,62836]) ).
thf(64420,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[64419]) ).
thf(64497,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( tc_nat @ ( tc_nat @ tc_prod ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than )
| ( A
!= ( tc_nat @ ( tc_nat @ ( C @ ( C @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[64420]) ).
thf(64566,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_Pair ) ) ) @ c_insert ) ) )
!= c_Wellfounded__Relations_Oless__than ),
inference(simp,[status(thm)],[64497]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv__iff1_0) ).
thf(664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_append ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(7279,plain,
! [A: $i] :
( ( A != c_UNIV )
| ( c_0 != v_Y )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,1456]) ).
thf(7280,plain,
( ( c_0 != v_Y )
| ~ ( tc_nat @ ( c_0 @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[7279:[bind(A,$thf( c_UNIV ))]]) ).
thf(7296,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ( c_0 != c_0 )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[360,343]) ).
thf(7297,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ c_Suc ) )
| ~ ( tc_nat @ ( c_0 @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[7296]) ).
thf(7298,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[7297:[bind(A,$thf( C @ c_Suc )),bind(B,$thf( C ))]]) ).
thf(7943,plain,
! [A: $i] :
~ ( tc_nat @ ( c_0 @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(simp,[status(thm)],[7298]) ).
thf(958,plain,
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( t_a @ ( v_X @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,736]) ).
thf(959,plain,
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( t_a @ ( v_X @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[958]) ).
thf(960,plain,
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_X )
| ( c_UNIV != v_x ) ),
inference(simp,[status(thm)],[959]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(696,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(188,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(720,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(2985,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[717,736]) ).
thf(2986,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[2985]) ).
thf(3002,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2986]) ).
thf(3015,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[3002]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(1974,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[824,299]) ).
thf(1975,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[1974]) ).
thf(1989,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_Y )
| ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= v_x ) ),
inference(simp,[status(thm)],[1975]) ).
thf(33344,plain,
! [A: $i] :
( ( A != tc_bool )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33219]) ).
thf(33345,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33344:[bind(A,$thf( tc_bool ))]]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff__iff1_0) ).
thf(807,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(2617,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ ( v_Z @ c_lessequals ) ) ) )
| ~ ( t_a @ tc_set @ ( C @ ( v_Y @ c_lessequals ) ) )
| ~ $true
| ( t_a @ tc_set @ ( C @ ( v_X @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[844,300]) ).
thf(2618,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ ( v_Z @ c_lessequals ) ) ) )
| ~ ( t_a @ tc_set @ ( C @ ( v_Y @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( C @ ( v_X @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[2617]) ).
thf(2619,plain,
( ~ ( t_a @ tc_set @ ( v_Z @ ( v_Y @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( v_Z @ ( v_X @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[2618:[bind(A,$thf( v_Z )),bind(B,$thf( t_a )),bind(C,$thf( v_Z ))]]) ).
thf(19698,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,4755]) ).
thf(19699,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( B @ c_Suc @ ( C @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19698]) ).
thf(19700,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[19699:[bind(A,$thf( tc_nat @ ( G @ c_Suc @ ( D @ c_plus ) ) )),bind(B,$thf( G )),bind(C,$thf( D ))]]) ).
thf(20265,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[19700]) ).
thf(270,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(886,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff__iff1_0) ).
thf(723,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(33751,plain,
! [A: $i] :
( ( A
!= ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption ) )
| ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33348]) ).
thf(33752,plain,
( ( c_0 @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33751:[bind(A,$thf( tc_bool @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(43,axiom,
! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
thf(395,plain,
! [A: $i] : ( tc_nat @ ( c_0 @ ( A @ c_Divides_Oop_Advd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff__iff2_0) ).
thf(839,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(1023,plain,
! [B: $i,A: $i] :
( ( A != tc_bool )
| ( c_List_Olist_ONil @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( B @ tc_List_Olist @ ( A @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[311,465]) ).
thf(1024,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_bool @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[1023:[bind(A,$thf( tc_bool ))]]) ).
thf(1129,plain,
! [A: $i] :
( ( c_List_Olist_ONil @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ tc_List_Olist @ ( tc_bool @ c_Nat_Osize ) @ ( c_0 @ c_less ) ) ) ),
inference(simp,[status(thm)],[1024]) ).
thf(125,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq__iff1_0) ).
thf(575,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(5580,plain,
! [A: $i] :
( ( A != tc_nat )
| ( ( c_0 @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,357]) ).
thf(5581,plain,
( ( ( c_0 @ ( c_0 @ ( c_0 @ c_plus ) ) )
= c_0 )
| ( tc_nat @ ( tc_nat @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[5580:[bind(A,$thf( tc_nat ))]]) ).
thf(14580,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ~ $true
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Z ) ),
inference(paramod_ordered,[status(thm)],[6138,326]) ).
thf(14581,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_List_Olist_ONil @ ( c_0 @ c_less ) ) )
!= ( tc_nat @ ( c_0 @ ( A @ c_less ) ) ) )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[14580]) ).
thf(14597,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( c_List_Olist_ONil != c_0 )
| ( c_0 != A )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[14581]) ).
thf(14603,plain,
( ( c_List_Olist_ONil != c_0 )
| ( c_UNIV != c_List_Olist_ONil )
| ( c_0 != v_Z ) ),
inference(simp,[status(thm)],[14597]) ).
thf(8533,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_Y ) ),
inference(paramod_ordered,[status(thm)],[5739,457]) ).
thf(8534,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_UNIV @ ( c_0 @ c_less ) ) ) )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[8533]) ).
thf(8580,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( B != c_UNIV )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[8534]) ).
thf(8585,plain,
! [A: $i] :
( ( ( tc_nat @ ( c_UNIV @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_Y ) ),
inference(simp,[status(thm)],[8580]) ).
thf(252,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
thf(850,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ c_Main_OusumE__2 ) ) ) @ c_Datatype__Universe_OIn1 ) ) ) )
| ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( B @ c_Main_OusumE__1 ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ousum ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(33757,plain,
! [A: $i] :
( ( A != tc_bool )
| ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,33348]) ).
thf(33758,plain,
( ( c_0 @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[33757:[bind(A,$thf( tc_bool ))]]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(607,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(321,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[320]) ).
thf(322,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = c_List_Olist_ONil ) ),
inference(lifteq,[status(thm)],[321]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(336,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( A
!= ( C @ ( A @ ( B @ c_append ) ) ) ) ),
inference(cnf,[status(esa)],[335]) ).
thf(337,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_List_Olist_ONil )
| ( ( C @ ( A @ ( B @ c_append ) ) )
!= A ) ),
inference(lifteq,[status(thm)],[336]) ).
thf(932,plain,
( ( ( t_a @ ( v_X @ ( v_x @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[297,299]) ).
thf(933,plain,
( ( t_a @ ( v_X @ ( v_x @ c_in ) ) )
!= ( t_a @ ( v_Y @ ( v_x @ c_in ) ) ) ),
inference(simp,[status(thm)],[932]) ).
thf(934,plain,
( ( t_a != t_a )
| ( v_X != v_Y )
| ( v_x != v_x ) ),
inference(simp,[status(thm)],[933]) ).
thf(935,plain,
v_X != v_Y,
inference(simp,[status(thm)],[934]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(923,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(21183,plain,
! [A: $i] :
( ( A != c_emptyset )
| ( c_0 != v_X )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,1279]) ).
thf(21184,plain,
( ( c_0 != v_X )
| ~ ( tc_nat @ ( c_emptyset @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[21183:[bind(A,$thf( c_emptyset ))]]) ).
thf(6071,plain,
! [A: $i] :
( ( A != tc_bool )
| ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,465]) ).
thf(6072,plain,
( ( c_0 @ class_Finite__Set_Ofinite )
| ( tc_nat @ ( tc_bool @ ( c_0 @ c_less ) ) ) ),
inference(pattern_uni,[status(thm)],[6071:[bind(A,$thf( tc_bool ))]]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff__iff1_0) ).
thf(639,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff__iff1_0) ).
thf(755,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(57112,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ~ $true
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(paramod_ordered,[status(thm)],[48433,470]) ).
thf(57113,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite )
!= ( A @ class_Finite__Set_Ofinite ) )
| ( A @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite ) ),
inference(simp,[status(thm)],[57112]) ).
thf(57114,plain,
tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ class_Finite__Set_Ofinite,
inference(pattern_uni,[status(thm)],[57113:[bind(A,$thf( tc_Product__Type_Ounit @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption @ tc_Datatype_Ooption ))]]) ).
thf(491,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[490]) ).
thf(19448,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( B @ c_plus ) ) ) )
| ( c_0 != c_0 )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[422,12829]) ).
thf(19449,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( tc_nat @ ( C @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( B @ c_plus ) ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(simp,[status(thm)],[19448]) ).
thf(19450,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(pattern_uni,[status(thm)],[19449:[bind(A,$thf( tc_nat @ ( J @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( D @ c_plus ) ) )),bind(B,$thf( D )),bind(C,$thf( J ))]]) ).
thf(20202,plain,
! [B: $i,A: $i] :
~ ( tc_IntDef_Oint @ ( tc_nat @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ c_Suc @ c_Nat_Osize ) @ ( A @ c_plus ) ) @ ( c_0 @ c_Divides_Oop_Advd ) ) ),
inference(simp,[status(thm)],[19450]) ).
thf(495,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(polarity_switch,[status(thm)],[494]) ).
thf(496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Datatype__Universe_OIn1 ) ) )
!= ( C @ ( B @ ( D @ c_Datatype__Universe_OIn0 ) ) ) ),
inference(lifteq,[status(thm)],[495]) ).
thf(21601,plain,
! [A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(paramod_ordered,[status(thm)],[425,1402]) ).
thf(21602,plain,
( ( c_emptyset != c_0 )
| ~ ( tc_nat @ ( c_Finite__Set_OFinites @ ( c_0 @ c_Divides_Oop_Advd ) ) ) ),
inference(pattern_uni,[status(thm)],[21601:[bind(A,$thf( c_Finite__Set_OFinites ))]]) ).
thf(486,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( D @ ( C @ ( E @ ( H @ c_Datatype__Universe_Odprod ) ) ) @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( G @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ ( F @ c_Datatype__Universe_OScons ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( H @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( G @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ tc_prod ) @ ( E @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[485]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
thf(882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(6881,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) )
| ~ $true
| ( c_0 != v_X ) ),
inference(paramod_ordered,[status(thm)],[5572,481]) ).
thf(6882,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) )
!= ( tc_nat @ ( c_emptyset @ ( c_0 @ c_less ) ) ) )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6881]) ).
thf(6924,plain,
! [B: $i,A: $i] :
( ( tc_nat != tc_nat )
| ( A != c_emptyset )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6882]) ).
thf(6933,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ ( c_emptyset @ c_plus ) ) )
!= c_0 )
| ( c_0 != v_X ) ),
inference(simp,[status(thm)],[6924]) ).
thf(74864,plain,
$false,
inference(e,[status(thm)],[809,56880,5136,468,33341,555,481,479,16501,19101,347,9180,893,63199,23194,518,6954,666,6142,683,33214,23240,34829,9337,449,379,4592,861,523,582,762,33219,9573,730,23483,33277,2622,741,13462,440,511,385,6401,8622,500,20312,472,71221,698,5005,23423,340,670,9184,18592,54276,1137,550,32069,20352,715,747,913,1458,18499,6138,782,301,320,436,8583,829,404,33511,898,709,64366,841,417,7734,55695,34975,21124,5342,389,570,64658,72941,36097,372,619,344,1279,64882,23711,1462,504,27725,23323,751,12606,357,542,460,902,853,8590,5605,33761,325,55689,28669,9039,1494,4756,9420,16809,33095,5338,1319,870,606,65948,8235,770,1398,416,1489,475,492,33517,789,443,376,7677,348,485,1136,834,13543,353,821,7899,2017,480,33754,634,61788,293,453,774,6932,396,6702,428,13725,13248,602,5572,33273,877,692,866,15799,2242,64875,527,312,307,23304,452,920,678,9340,661,546,925,534,798,512,439,20500,62196,12474,381,5487,366,9041,5334,63201,910,825,778,9075,598,561,297,407,429,54272,729,55063,17467,19950,334,33163,302,5956,820,392,1487,19021,815,33168,361,879,329,63232,14681,889,461,456,324,916,467,847,484,23577,58523,2663,435,522,830,62836,493,757,5658,63236,2112,1402,519,34693,615,725,403,8619,33348,29448,356,593,420,23708,22322,67418,610,13899,56561,471,884,20248,11860,24505,537,476,642,526,637,547,18016,489,837,647,701,1456,654,32265,7738,457,721,61093,503,55707,985,8587,5823,569,10302,371,14249,343,63200,792,805,508,311,9044,765,16169,33109,6931,530,5126,7074,926,633,360,44943,541,794,586,1996,718,888,298,32233,425,20236,5138,7512,9181,33520,444,9072,8215,412,513,1146,5451,824,856,63489,6001,745,689,5979,296,375,733,56714,423,694,402,8900,7736,12301,49206,4758,545,413,584,6140,562,904,56556,22702,772,56729,20486,33165,8124,743,875,711,8027,29225,33856,48103,71226,787,466,335,70918,45474,33343,27507,350,540,672,391,1139,382,33515,572,63571,313,6937,713,498,604,6144,19121,784,419,1524,1144,616,599,863,9575,900,406,58694,681,7514,21772,736,7255,451,567,737,318,509,24499,880,649,434,477,494,631,323,726,5656,626,2252,462,387,811,2182,345,552,535,5730,621,20298,46989,520,895,58704,10380,668,33756,399,3110,780,455,2369,608,6704,299,16467,505,431,14947,8457,912,685,521,768,827,2051,636,695,33275,6930,868,9916,306,56719,14800,6212,922,5463,26591,426,680,548,14724,18434,749,939,27235,1145,355,9507,458,6083,473,48433,2054,490,675,45204,531,927,374,1134,487,1990,516,5003,28067,11230,56571,776,295,67412,872,12313,414,2732,739,10392,15220,20080,525,557,5716,580,855,55632,705,17968,1400,707,9037,327,19954,47787,23228,24357,2175,68352,331,441,717,502,21679,463,338,33958,6421,370,470,6313,10739,8024,29192,22302,544,907,6701,703,656,864,5453,9930,22222,446,68346,612,497,4671,12829,600,20077,859,54228,54270,10714,845,465,55642,14678,688,524,23261,759,891,47480,1316,450,1459,19493,7316,363,931,539,482,2870,1289,844,68314,7732,69005,813,517,319,36267,8584,390,632,401,786,588,699,7044,304,23497,36447,378,9510,478,4404,1513,5739,832,33280,549,536,568,23330,929,11755,35934,9421,55627,800,752,58711,4670,33216,410,818,9070,735,300,33513,5728,315,58372,17140,405,58708,422,5477,14070,564,326,341,4755,64566,474,664,63230,7280,7943,960,696,720,796,3015,305,294,918,1989,33345,506,358,807,2619,532,20265,886,415,728,62784,464,596,723,5958,10304,442,33752,395,839,332,1129,9038,575,5581,528,14603,8585,24481,850,9335,34564,501,33758,369,607,322,803,337,469,935,923,309,543,21184,560,6072,639,755,57114,491,20202,1468,496,364,21602,486,34070,882,6933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET834-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.42 % Computer : n006.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 08:19:29 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.84/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.82/1.39 % [INFO] Parsing done (389ms).
% 2.26/1.41 % [INFO] Running in sequential loop mode.
% 2.96/1.79 % [INFO] eprover registered as external prover.
% 3.11/1.80 % [INFO] Scanning for conjecture ...
% 3.37/1.95 % [INFO] Found a conjecture (or negated_conjecture) and 1357 axioms. Running axiom selection ...
% 4.00/2.09 % [INFO] Axiom selection finished. Selected 286 axioms (removed 1071 axioms).
% 4.84/2.21 % [INFO] Problem is propositional (TPTP CNF).
% 4.84/2.22 % [INFO] Type checking passed.
% 4.84/2.22 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 192.52/53.45 % External prover 'e' found a proof!
% 192.52/53.45 % [INFO] Killing All external provers ...
% 192.52/53.45 % Time passed: 52891ms (effective reasoning time: 52040ms)
% 192.52/53.46 % Axioms used in derivation (286): cls_Finite__Set_Ofinite__converse__iff1_0, cls_IntDiv_Ozdvd__0__right_0, cls_Finite__Set_Ofinite__Union_0, cls_Datatype__Universe_Ousum__In1I_0, cls_Datatype__Universe_OuprodI_0, cls_Nat_Ole__0__eq__iff1_0, cls_SetInterval_OgreaterThan__subset__iff__iff1_0, cls_List_Ofinite__set_0, cls_Finite__Set_Ofinite__Un__iff1_1, cls_Datatype__Universe_OdprodE_0, cls_SetInterval_OlessThan__iff__iff2_0, cls_List_Oset__empty2__iff2_0, cls_List_Oappend__in__lists__conv__iff2_0, cls_Datatype__Universe_Odsum__In0I_0, cls_List_Oset__empty2__iff1_0, cls_List_ONil__notin__lex__iff1_0, cls_Relation_OImageI_0, cls_SetInterval_OatLeast__subset__iff__iff2_0, cls_Set_OsubsetI_1, cls_Sum__Type_OInr__not__Inl__iff1_0, clsarity_prod_0, cls_List_Olists_ONil_0, cls_Set_OInterD_0, cls_List_ONil__is__append__conv__iff2_0, cls_SetInterval_OgreaterThan__iff__iff2_0, clsarity_nat_7, cls_Sum__Type_OInr__eq__iff1_0, cls_Set_OemptyE_0, cls_Set_OUNIV__not__empty__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff2_0, cls_Wellfounded__Recursion_Owf__insert__iff1_0, cls_Finite__Set_OFinites_OemptyI_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff1_0, cls_List_Oappend__self__conv2__iff1_0, cls_Relation_OImageE_0, cls_Datatype__Universe_Ousum__In0I_0, cls_IntDiv_Ozdvd__0__left__iff2_0, clsrel_Orderings_Olinorder_4, cls_Nat_Oless__Suc0__iff1_0, cls_Set_Osingleton__insert__inj__eq__iff1_1, cls_Datatype__Universe_OusumE_2, cls_Datatype_Ooption_Oinject__iff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Set_Osingleton__inject__dest_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_1, cls_Set_OUnionE_1, cls_Nat_Oadd__is__0__iff1_1, clsarity_sum_0, cls_Finite__Set_OFinites_OinsertI_0, cls_Nat_Oless__irrefl_0, cls_IntDiv_Ozminus__dvd__iff__iff1_0, clsarity_set_2, cls_Nat_Onot__less0__iff1_0, cls_List_Olistrel__Nil1_0, clsarity_nat_3, cls_Datatype__Universe_OIn1__eq__iff1_0, cls_Set_OComplI_0, cls_Relation_OconverseE_1, cls_Finite__Set_Ofinite__Int_0, cls_Nat_Oadd__gr__0__iff2_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, cls_Nat_Oneq0__conv__iff2_0, cls_Sum__Type_OPlusE_0, cls_Nat_Oadd__is__0__iff2_0, cls_List_ONil__is__append__conv__iff1_0, cls_Relation_Orel__compE_0, cls_Finite__Set_Ofinite__Pow__iff__iff1_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_1, cls_Sum__Type_OInlI_0, clsarity_IntDef__Oint_0, cls_Infinite__Set_Onat__not__finite_0, cls_Set_OpsubsetI_0, cls_Relation_Oconverse__iff__iff2_0, cls_Set_Osubset__refl_0, cls_List_Olist_Oinject__iff1_0, cls_Relation_ORangeE_0, cls_SetInterval_OlessThan__iff__iff1_0, cls_Set_OInterI_1, cls_Nat_OSuc__Suc__eq__iff1_0, cls_List_Oset__empty__iff2_0, cls_Set_OUnCI_1, cls_Product__Type_OPair__eq__iff1_0, cls_Set_OinsertCI_0, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, cls_Set_Osingleton__insert__inj__eq_H__iff2_0, cls_Set_OPow__iff__iff2_0, cls_List_Oappend__in__lists__conv__iff1_0, cls_Finite__Set_Ofinite__converse__iff2_0, cls_SetInterval_OatMost__iff__iff2_0, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, cls_Nat_Ole__0__eq__iff2_0, cls_Datatype__Universe_OIn0__not__In1__iff1_0, cls_Relation_OdiagI_0, cls_Set_OCompl__subset__Compl__iff__iff2_0, cls_Datatype__Universe_OdprodE_1, cls_Set_OUNIV__I_0, cls_Set_OCompl__eq__Compl__iff__iff1_0, cls_Set_OsubsetI_0, cls_Sum__Type_OPlusE_3, cls_Finite__Set_Ofinite__Diff__insert__iff1_0, cls_List_OlistsE_0, cls_List_Olength__0__conv__iff2_0, cls_Divides_Odvd__0__left__iff__iff2_0, cls_Finite__Set_Ofinite__Un__iff1_0, cls_List_Oself__append__conv__iff2_0, cls_SetInterval_OatMost__eq__iff__iff1_0, cls_Relation_ODomainI_0, cls_Set_OinsertE_0, cls_Set_Onot__psubset__empty__iff1_0, cls_Set_OUnE_0, cls_SetInterval_OlessThan__subset__iff__iff2_0, cls_List_Owf__lex_0, cls_SetInterval_OgreaterThan__subset__iff__iff2_0, cls_Datatype__Universe_OusumE_1, cls_Set_OComplD__dest_0, cls_Set_OUn__empty__iff1_1, cls_Relation_Orel__compE_2, cls_Nat_OZero__not__Suc__iff1_0, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, clsarity_set_3, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_SetInterval_OatMost__subset__iff__iff2_0, cls_SetInterval_OatLeast__subset__iff__iff1_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Set_OUn__empty__iff1_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Wellfounded__Recursion_Owf__insert__iff2_0, cls_Set_Oempty__subsetI_0, cls_Finite__Set_Ofinite__Int_1, cls_Relation_OIdI_0, cls_SetInterval_OlessThan__eq__iff__iff1_0, clsarity_IntDef__Oint_31, cls_List_Oappend__is__Nil__conv__iff2_0, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_Nat_OSuc__less__eq__iff2_0, cls_Divides_Odvd__0__left__iff__iff1_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olength__greater__0__conv__iff1_0, cls_List_Oappend1__eq__conv__iff1_1, cls_Set_OsubsetD_0, cls_Product__Type_OPair__eq__iff1_1, cls_Nat_Oadd__gr__0__iff2_1, cls_List_Osame__append__eq__iff1_0, cls_Set_OsingletonI_0, cls_Nat_Oless__Suc0__iff2_0, cls_Wellfounded__Relations_Oless__than__iff__iff1_0, cls_Set_Osubset__antisym_0, cls_Wellfounded__Recursion_Oacyclic__insert__iff1_0, cls_List_Oself__append__conv__iff1_0, cls_SetInterval_OatLeast__iff__iff2_0, cls_Nat_Ozero__less__Suc_0, cls_List_Oin__listsI_1, cls_SetInterval_OatMost__subset__iff__iff1_0, cls_Datatype_Oelem__o2s__iff1_0, cls_Relation_OconverseE_0, cls_List_Olength__greater__0__conv__iff2_0, cls_Datatype__Universe_OuprodE_2, clsrel_Orderings_Oorder_0, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Relation_Oconverse__iff__iff1_0, cls_Datatype__Universe_OIn1__not__In0__iff1_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_0, cls_List_Olist_Oinject__iff1_1, cls_Datatype__Universe_OuprodE_0, cls_Set_ODiffE_0, cls_Datatype__Universe_OusumE_0, cls_SetInterval_OatMost__iff__iff1_0, cls_Datatype_Oelem__o2s__iff2_0, cls_SetInterval_OgreaterThan__eq__iff__iff1_0, cls_Sum__Type_OInl__not__Inr__iff1_0, cls_Infinite__Set_Oatmost__one__unique_0, clsarity_set_1, cls_Datatype__Universe_OdprodE_2, cls_Relation_ORangeI_0, cls_List_Oset__empty__iff1_0, cls_Nat_OSuc__le__mono__iff1_0, cls_List_Oself__append__conv2__iff2_0, cls_Set_OIntE_1, cls_Relation_Opair__in__Id__conv__iff1_0, cls_Nat_Onot__add__less1__iff1_0, cls_Set_OIntI_0, cls_Finite__Set_Ofinite__Union_1, cls_Sum__Type_OPlusE_2, cls_Set_Osingleton__insert__inj__eq__iff2_0, cls_IntDiv_Ozdvd__0__left__iff1_0, cls_Wellfounded__Relations_Oless__than__iff__iff2_0, cls_Nat_Oadd__gr__0__iff1_0, cls_Divides_Odvd__0__right_0, cls_IntDef_Oint__int__eq__iff1_0, cls_IntDiv_Odvd__zminus__iff__iff1_0, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_List_Olist_Odistinct__2__iff1_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_Finite__Set_Ofinite__Diff__insert__iff2_0, cls_Datatype__Universe_OdprodI_0, cls_SetInterval_Ofinite__greaterThanLessThan_0, clsarity_fun_1, cls_List_OlistsE_1, cls_List_Oappend__self__conv2__iff2_0, clsarity_nat_12, cls_Nat_OSuc__le__mono__iff2_0, cls_IntDiv_Odvd__zminus__iff__iff2_0, cls_List_Oappend__self__conv__iff2_0, cls_SetInterval_OgreaterThan__iff__iff1_0, cls_List_Oappend__same__eq__iff1_0, clsarity_IntDef__Oint_5, cls_Set_OCompl__subset__Compl__iff__iff1_0, cls_Set_ODiffI_0, cls_Orderings_Oorder__less__irrefl__iff1_0, cls_Sum__Type_OInrI_0, cls_Datatype__Universe_Odsum__In1I_0, clsarity_IntDef__Oint_62, cls_Set_OUn__empty__iff2_0, cls_Datatype__Universe_OuprodE_1, cls_Set_OpsubsetE_0, cls_Set_OUnionI_0, cls_Datatype__Universe_OScons__Scons__eq__iff1_1, cls_List_Olistrel__Nil2_0, cls_Relation_Orel__compI_0, cls_Finite__Set_Ofinite__Pow__iff__iff2_0, cls_List_Oappend__is__Nil__conv__iff1_0, cls_Datatype__Universe_OIn0__eq__iff1_0, cls_Wellfounded__Recursion_Oacyclic__converse__iff2_0, cls_Nat_OSuc__less__eq__iff1_0, cls_Relation_OdiagE_1, clsarity_nat_9, cls_Relation_OImage__singleton__iff__iff1_0, cls_List_ONil2__notin__lex__iff1_0, cls_List_Oself__append__conv2__iff1_0, cls_Nat_Oneq0__conv__iff1_0, cls_Set_OInterI_0, cls_List_Olist_Odistinct__1__iff1_0, clsarity_bool_0, cls_Nat_Oadd__is__0__iff1_0, cls_SetInterval_OatLeast__eq__iff__iff1_0, cls_Orderings_Oorder__class_Oaxioms__1_0, clsarity_Product____Type__Ounit_0, cls_IntDef_Onegative__zle_0, cls_Sum__Type_OPlusE_1, cls_Set_OUnionE_0, cls_Relation_ODomainE_0, clsrel_Orderings_Olinorder_3, cls_List_Oin__listsI_0, cls_Divides_Odvd__1__left_0, cls_SetInterval_OatLeast__iff__iff1_0, cls_Wellfounded__Recursion_Owf__insert__iff1_1, cls_List_Oappend1__eq__conv__iff1_0, clsarity_set_0, clsarity_Datatype__Ooption_0, cls_Nat_OSuc__not__Zero__iff1_0, cls_List_Oin__listsD__dest_0, cls_Set_OPow__iff__iff1_0, cls_Nat_Ole0_0, cls_Set_Osingleton__insert__inj__eq__iff1_0, cls_Sum__Type_OInl__eq__iff1_0, cls_Set_Osingleton__insert__inj__eq_H__iff1_0, cls_Relation_OImage__singleton__iff__iff2_0, cls_Datatype__Universe_OusumE_3, cls_List_Olength__0__conv__iff1_0, clsarity_fun_0, cls_Relation_OIdE_0, clsarity_nat_2, cls_Set_OpsubsetE_1, cls_Nat_OlessI_0, cls_SetInterval_Ofinite__atMost_0, cls_Set_OIntE_0, cls_Relation_Orel__compE_1, clsarity_set_4, cls_List_Oappend__is__Nil__conv__iff1_1, cls_Finite__Set_Ofinite__Un__iff2_0, cls_Nat_Onot__add__less2__iff1_0, cls_Set_OinsertCI_1, cls_Set_ODiffE_1, cls_IntDef_Onegative__zless_0, cls_List_ONil__is__append__conv__iff1_1, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_List_Oappend__self__conv__iff1_0, cls_IntDiv_Ozminus__dvd__iff__iff2_0, cls_Set_OUnCI_0, cls_List_Olists_OCons_0, cls_List_Oappend__in__lists__conv__iff1_1, cls_SetInterval_OlessThan__subset__iff__iff1_0
% 192.52/53.46 % No. of inferences in proof: 1854
% 192.52/53.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 52891 ms resp. 52040 ms w/o parsing
% 193.87/53.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 193.87/53.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------